Pith. sign in

Paper Citation Record · LEDGER

A comment on the equation $n!!=a_1!!\cdots a_t!!$

As of 12 August 2026, this Paper Citation Record lists 68 of 68 outbound references and 0 inbound Pith citation observations for arXiv:2604.09730.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2604.09730 v1

Coverage vector

measured 68 of 68 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-10T18:17:05.380100Z

measured 68 of 68 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

68 of 68 outbound references displayed

  • verified exact4
  • verified fuzzy58
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9ded7cd5-5253-449f-ae1e-1b0a009ab2b9 · outbound

This paper cites Alzer and F.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Alzer and F

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.530393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:1089c65127000a94fed4ccf6d6696b34369b5f95d29a18a95faf9dc7f7327521

Observation de0439ea-dd77-4891-b531-d22295e9d2df · outbound

This paper cites Baker: A sharpening of the bounds for linear forms in logarithms.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Baker: A sharpening of the bounds for linear forms in logarithms

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.569515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:283237a6cea110810e673a03e33ebeb9db9bb2b64ee409950b87dc30db6e0355

Observation c029f850-2828-49ed-8217-e70bb20c4c7e · outbound

This paper cites Bachman, Introduction of p -adic numbers and valuation theory, Academic Press, New York.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Bachman, Introduction of p -adic numbers and valuation theory, Academic Press, New York

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.523051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:268284f8d7ba5143e39a5002fec0c02ba32d092ed85fc837f3757e87466a2620

Observation 16a4cdd9-37d2-4b73-8c0c-ca6623ea5e66 · outbound

This paper cites Baczkowski, M.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Baczkowski, M

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.535775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:ce3ff1d717493d060c79624e6148451adf505a07b5dc008767d27026dc25d006

Observation 515d1b75-59fe-4109-b9ad-cf55b1afccfe · outbound

This paper cites Baczkowski and S.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Baczkowski and S

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.543804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:b565986cbcfe273854f849ae0a9d27c163ca322d17e6d9a97e894633e87014ce

Observation 0d67f955-2e7a-431b-99f3-71c68b71e915 · outbound

This paper cites Baker, Experiments on the abc-conjecture.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Baker, Experiments on the abc-conjecture

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.525550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:13226d17f1b1a81b345fb2895626e9f33a27f895c8ef48fafeb2b05bae57d067

Observation 2193c45d-2c50-4b9e-8af9-17b6e7a1286c · outbound

This paper cites an unresolved cited work.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-05-17T06:01:35.557664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:9d27f12b52f68fe12140ad82fe9c32f8d8fb5386cac644994a4c51add180cf03

Observation 7693a354-6abc-4e89-b051-230e0b33a577 · outbound

This paper cites Bennett, et al., Explicit bounds for primes in arithmetic progressions.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Bennett, et al., Explicit bounds for primes in arithmetic progressions

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.527888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:838f5cf982aeed7fea98181ca9cf2750a366f4d97f7fa3666c6a4ae7c95e1b23

Observation c04980ef-8577-4276-a532-f2a8c8f4b324 · outbound

This paper cites an unresolved cited work.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-05-17T06:01:35.552061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:27b20e780890978a4ee915faeb3268b88a3ccd165a95cddccf379da1dc8dc7c2

Observation 52234963-f146-4993-ade6-df2f1605e200 · outbound

This paper cites Bhargava, P-orderings and polynimial functions on arbitrary subsets of Dedekind rings.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Bhargava, P-orderings and polynimial functions on arbitrary subsets of Dedekind rings

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.541188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:afc664bb2e7e93d3f617014de5ef07258a139fa1e03f7dfce04580f4dba1776d

Observation fc1c8efc-3998-46cc-9500-3a2ce188c2dd · outbound

This paper cites Berend and C.F.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Berend and C.F

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.538474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:c6e2407218dcd07d41c77a79c558a0d0653def88093110706f25b2cd0c216649

Observation a9095cf2-6da5-4b50-93d3-422d949d5205 · outbound

This paper cites Berend and J.E.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Berend and J.E

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.546510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:7f8adf3e8bca1681a83a9b02a06647ff2082b8386703de236fc5dbb7af3a2a67

Observation 08ff981e-1e82-4027-b1a3-c115266431ec · outbound

This paper cites Berndt and W.F.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Berndt and W.F

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.533117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:a1f6033f6b0d8236d3d2157d82962fd842dd4de5adcf1f57fd068f11ab89523e

Observation c8c50fcc-738d-4fe4-b624-298eeadaa0db · outbound

This paper cites Brocard: Question 1532.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Brocard: Question 1532

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.560576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:416a886c8afe564fb5f4f3f42ce364a03a6589e0a82a04798232b93b24a86f68

Observation ab7fa1cb-945f-46e6-b11e-5a05aa227d17 · outbound

This paper cites Dusart, Autour de la fonction qui compte le nombre de nombre premiers.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Dusart, Autour de la fonction qui compte le nombre de nombre premiers

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.554947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:342177e5cc94a5a27e877930f735c4a2cc20a252327460b1a859f7b7ec57eff2

Observation 009e6a85-3e22-4c2a-8975-dba09be6e1f6 · outbound

This paper cites Dusart, In\'egalit\'es explicites pour (X), (X), (X) et les nombres premiers.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Dusart, In\'egalit\'es explicites pour (X), (X), (X) et les nombres premiers

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.549102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:63772c7b2c3f776dcc333f857e953d326387511f78657ca37e8f3ca71bb87f26

Observation 6e510bf0-f57f-4abb-b278-f0d969928dcd · outbound

This paper cites Erd o s and R.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Erd o s and R

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.566178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:0fa05133e1211aff0ffc8f562cb6bf58e6cae5bf684cc177949dd1aa5e7a5b53

Observation d52998c1-606e-4376-be20-6447662b926b · outbound

This paper cites Erd o s, On consecutive integers.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Erd o s, On consecutive integers

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.563260Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:53fe7e99688f3b79c3241d7ec23bd78b6caf87870e7b6799ad4ac5ec416eebaa

Observation 1c8787b8-4ed2-4295-86c3-9896abf0fde3 · outbound

This paper cites Erd o s\ et al., On the number of divisors of n! , in Analytic number theory, Vol.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Erd o s\ et al., On the number of divisors of n! , in Analytic number theory, Vol

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.395629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:9ddb0f68521bc5df0ea5997afdec548ef21d283c747d58a5fb6014386cbe906c

Observation ac537e49-119a-4d5b-b57b-49a14d7a7303 · outbound

This paper cites Bugeaud, M.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Bugeaud, M

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.449731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:4fcf7c912374760d8320b42fd72bd2f88c32fb397543d29335dff898e95a18b4

Observation 3346a683-360a-40a2-a9bf-ff4b7219e1fd · outbound

This paper cites an unresolved cited work.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-05-17T06:01:35.458127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:0b4099da64b1aefa2ea460a95d38a02e1f402ae31bc956986632cf7d5389aa0d

Observation 33eb0896-efc0-499c-afee-83d6585d88c8 · outbound

This paper cites Dabrowski, On the equation n!+A=y^2.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Dabrowski, On the equation n!+A=y^2

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.439043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:9d8d3b3aaf9e5d785464e50a4df2714675e9201a2769162197f0747eaf5c2ae1

Observation 9a8bfecd-dca6-41a5-a17b-bfefbd93c587 · outbound

This paper cites Dabrowski: On the Brocard--Ramanujan problem and generalizations.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Dabrowski: On the Brocard--Ramanujan problem and generalizations

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.408828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:eed975c84a8a7173d160c02573002e9cd7d0fe1cd1b05fc70596728e491b3f53

Observation 67e46cfc-b4d9-453c-8c2c-22d5dff03679 · outbound

This paper cites Dabrowski and M.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Dabrowski and M

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.435304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:4b6ac1222db4adb7c731a68fbe5ae4edba29b9b9228d11ef34cc4d1b987449eb

Observation 60aafbac-9b30-47dc-9095-c2d86b2f4356 · outbound

This paper cites Epstein and J.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Epstein and J

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.427171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:398a87f713ed5da20378e6ee43347aac9666d17ef23403daa41951b8d46f936f

Observation d3342bf4-049a-422f-b623-af8cc0e86a17 · outbound

This paper cites Dufour and O.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Dufour and O

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.407439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:bd02d0599a12e0daae9e0ab42d7162a039ac84ef7ee45c13238f9a609ae153e6

Observation 7a2522f7-ca49-4e69-bdcf-c44cfb4a5c69 · outbound

This paper cites an unresolved cited work.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-05-17T06:01:35.412578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:b3887660069f06ea664a0cff00089b22e5c380264b42db9bfbb01f756070b8bc

Observation c95e9ebe-1756-4dbe-a885-850167faebb9 · outbound

This paper cites Hardy and E.M.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Hardy and E.M

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.415901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:30ed55740a138811a22d3b091cd6bc2da8a4b353238bbf6d217a2e771fdcd56d

Observation 4078d81a-8613-48f8-b35a-1fa2e64cac37 · outbound

This paper cites Janusz, Algebraic number fields, Academic Press, New York and London (1973).

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Janusz, Algebraic number fields, Academic Press, New York and London (1973)

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.414431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:a6fe3a0a7c30636b64331c4519247322bedb0265b1c8ec50916eebdb69ce698b

Observation 30a894ef-6c16-4e09-843a-3500eb0446e6 · outbound

This paper cites Erd o s and R.L.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Erd o s and R.L

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.455330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:f4ec6cfd51eeed58a44e19dac11dd1544919f7e7f34c0fe0c1ee7d029c93ca13

Observation 88150f95-8b29-4696-be5e-58e3debe7e9c · outbound

This paper cites Kihel and F.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Kihel and F

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.511526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:ffddde0853ce488a789eb43c87417167885ee39fb3a51197fc90a8b589cea854

Observation d598a8f8-18e8-4c4f-8922-b747c6fb5b1c · outbound

This paper cites Lang: Old and new conjectured diophantine inequalities.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Lang: Old and new conjectured diophantine inequalities

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.401740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:6a2b3f303e0e8b9540fca9e13e9cc0ad7f18b7abb5d14abcebba77e9206b2c62

Observation 08fbcfb9-b433-432b-8b73-a24ee42b7322 · outbound

This paper cites Halberstam and H.-E.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Halberstam and H.-E

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.514370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:132d9db1c34c0d006f3fa70774ede198328f9dd0784ce706ca2525d6c2b103a2

Observation 163730bd-131c-4b4a-9953-2e1180c69aa3 · outbound

This paper cites Gawron, A note on the Diophantine equation P(z)=n!+m!.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Gawron, A note on the Diophantine equation P(z)=n!+m!

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.388293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:1052cf75863e305ee95ebb130e72baca571e0dcd12376743789ed6851da1aba4

Observation 098573ae-7900-47bf-87da-d169575cc2a4 · outbound

This paper cites Guy, Unsolved problems in number theory.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Guy, Unsolved problems in number theory

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.425103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:702172f659351a4b661ae51c4ecf076affe61d60881823be820cdee082ad97da

Observation 5f3dc721-c61a-4296-a46f-88fb53e01d71 · outbound

This paper cites Lang, Old and new conjectured Diophantine inequalities.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Lang, Old and new conjectured Diophantine inequalities

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.444195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:12dd6b6f7548c5cbdfdeea20e1de1b460ca3669309a9a8d402d8e84fbbd95dc0

Observation 8ee39138-4827-4671-8268-c519e1749a40 · outbound

This paper cites Luca, Equations involving arithmetic functions of factorials.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Luca, Equations involving arithmetic functions of factorials

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.398486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:06f29e94ad2b81ce732614fec5113cc73a284ff8574157c3e24c04404ddc099f

Observation 4f7adc7f-bd53-48b5-954e-5a9617f4fe8d · outbound

This paper cites Laishram and T.N.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Laishram and T.N

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.505962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:3d867d19cbc35359f102b9d4504316fc4eaf0e8bd212d56cd0dd4989740330e4

Observation 2b2890ff-f8db-49f2-83c4-d2340315fde9 · outbound

This paper cites Luca, The Diophantine equation P(x)=n! and a result of M.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Luca, The Diophantine equation P(x)=n! and a result of M

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.503196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:b941f043f9ece7ab1354cad196ce1555524d1f917f7076c8f2a818c5a6b0ed33

Observation 0f5f891f-7fff-43ba-9647-f2abb81bf1ec · outbound

This paper cites Luca, On factorials which are products of factorials.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Luca, On factorials which are products of factorials

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.517412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:516f9b4fead0ef17be7db1c4de79e6bb368496c4f2dbd5f851ec424f122cdfec

Observation e4b6c1ce-4615-4bd1-95fd-b6a77b4ebae4 · outbound

This paper cites an unresolved cited work.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-05-17T06:01:35.500376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:dcb1bdb277fe194bc34b29fa2925fe51f66c0e5f9fb7eb2e75e8b6ffce988373

Observation e5c961a3-fa3b-4376-b3a7-637538b80af2 · outbound

This paper cites Luca, On the Diophantine equations f(n)=u!+v!.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Luca, On the Diophantine equations f(n)=u!+v!

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.520323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:d65288fa729e3757e3ada778a0e0412a173bc125f7712779b9adfde7d9093a8e

Observation 19a49dc1-57ee-4e31-b90a-770ef24b32a4 · outbound

This paper cites Matson, Brocard's problem 4th solution search utilizing quadratic residues.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Matson, Brocard's problem 4th solution search utilizing quadratic residues

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.487587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:b7f5f085a024c6bbc1c9d77f8b27aaf73fa9a180631e2a8c3c47dd368cf3c7c3

Observation ffef8088-4d8e-4e8e-98b0-9e8994944dd6 · outbound

This paper cites Makki Naciri, On the variant Q(n!)=P(x) of the Brocard--Ramanujan Diophantine equation.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Makki Naciri, On the variant Q(n!)=P(x) of the Brocard--Ramanujan Diophantine equation

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.478155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:d39bace937cc1019f1584a67df9497430acb0288be21495db8f11ad12aba409c

Observation 53180916-556d-47fc-994b-cc69e1469042 · outbound

This paper cites Makki Naciri, On the Brocard-Ramanujan equation with 7-free integers and prime powers.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Makki Naciri, On the Brocard-Ramanujan equation with 7-free integers and prime powers

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.484487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:9d31b8e6f8a5a1b0020a142363743d63b97c556d2a386b8e128b8cca766b1446

Observation 827b7864-f12c-40e3-87c0-95b09dab8658 · outbound

This paper cites an unresolved cited work.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-05-17T06:01:35.475273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:54c19cf338993d63167fd2be65c7b74736ef5224ff825912c5792c4fbc0821b5

Observation b745b8da-5188-4d10-a615-f0662f30b245 · outbound

This paper cites Nair and T.N Shorey, On products from blocks of consecutive odd primes.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Nair and T.N Shorey, On products from blocks of consecutive odd primes

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.469970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:2c68fe5d369e98e85ede42cef5312fa83f0cd82308fe45a801d8d179f1fa784d

Observation 1530f752-be66-4719-86ee-b003d1fceb2b · outbound

This paper cites Novakovi\'c, Diophantine equations involving double factorials.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Novakovi\'c, Diophantine equations involving double factorials

Reference 48

Resolution
verified exact
arxiv_id, observed 2026-05-11T05:10:54.749183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:0699ffac5feb7526c2d25893f2760bb1dd629218628eddcf4ccc0908ea333dff

Observation fff2556d-252e-4bc1-8efc-fa92b03b74cf · outbound

This paper cites Novakovi\'c, A note on some polynomial-factorial Diophantine equations.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Novakovi\'c, A note on some polynomial-factorial Diophantine equations

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.449498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:4dac4b4de13156704f47edf9c2f326ccb770ed427fbba5130499dc22a0b4727f

Observation 1a566883-8133-4111-a713-e7cbfa5e2be5 · outbound

This paper cites Administrative Law's Fourth Settlement: AI and the Scrutable State.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Administrative Law's Fourth Settlement: AI and the Scrutable State

Reference 50

Resolution
verified exact
arxiv_id, observed 2026-07-27T01:19:56.859635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:516799ad9f18ee69260d2e699a4e6b048330e8bb93306fbf7f7a4a077710648d

Observation 6d0bd9ff-9343-48cb-aec3-ce03993f74d7 · outbound

This paper cites On the diophantine equation $An!+Bm!=f(x,y)$.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ On the diophantine equation $An!+Bm!=f(x,y)$

Reference 51

Resolution
verified exact
arxiv_id, observed 2026-05-11T05:10:54.775098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:25aceee0abbee39811d8764f154fcdb3a0fea442d2582eb11afba51e2f32576e

Observation 7d31df3f-b4a9-48c6-b1b5-c9cfe0918f98 · outbound

This paper cites Novakovi\'c, The Diophantine equation P(x)= r i=1 H_ n_i.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Novakovi\'c, The Diophantine equation P(x)= r i=1 H_ n_i

Reference 52

Resolution
verified exact
arxiv_id, observed 2026-05-11T05:10:54.742014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:734f7e03df7e372f2a479079cb893f229cc134d483a67b62d7926c12d024459e

Observation 27586a43-4cbf-461d-8267-4b3f10e31402 · outbound

This paper cites Overholt, The Diophantine equation n!+1=m^2.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Overholt, The Diophantine equation n!+1=m^2

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.463638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:0d999e7480ca81d133b39add620fbec811f89c771046fd287f3000826f3c0a1a

Observation 92da070b-36a4-4a77-94cc-da9eb1043f62 · outbound

This paper cites Pollack and H.N.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Pollack and H.N

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.472609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:c3a3e418b7506b00f1fe145b289b3ce278d1a90c86f94650270193c2f91d0877

Observation 2aadbf4d-2f6f-43c2-ab1a-ca561b3047fe · outbound

This paper cites Ramanujan, Question 469.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Ramanujan, Question 469

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.489914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:1d29408d4375097b268edfb1c449c439aaa4e3393714654b642f084e79b5c9a3

Observation 99d6b2c2-c2f7-42e1-a239-df80b1f1da70 · outbound

This paper cites Rosser and L.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Rosser and L

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.508900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:128733ea5d94fcbabb18d778fc64f665e65441d635db6d8b8626f544dbf45346

Observation 49fb0416-b208-4cb5-9ba8-307f9dd0c269 · outbound

This paper cites Saunders, Diophantine equations involving the Euler totient function.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Saunders, Diophantine equations involving the Euler totient function

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.460832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:1b33c138603b7d9a1ec5e831ea7a03e82ea2ec140e678229f48c684e3ce8db22

Observation 7e1efc6d-aed3-411b-a697-6d2efbd395df · outbound

This paper cites Shorey: Diophantine approximations, Diophantine equations, transcendence and applications.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Shorey: Diophantine approximations, Diophantine equations, transcendence and applications

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.466746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:2cb3f03dbb1de8f84f3a05abd645b1cb36b569e2cbaa58f0ca5acd700b6de34f

Observation 1b6f2cf1-b24b-48df-aadd-54cbb51961e6 · outbound

This paper cites Shorey and R.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Shorey and R

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.452660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:65f669d1002a8ca131b92bce55a280ce9972ce365a735157989aff5c5d4f6972

Observation bcee3b06-ab50-4ad0-932d-eaccafd1dde5 · outbound

This paper cites Siksek: Diophantine equations after Fermat's last theorem.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Siksek: Diophantine equations after Fermat's last theorem

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.492572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:c4749c9e87f3085a15b63cc7d10d4e7f48d226a153df9a6556222e053947ba5f

Observation 5ddbe455-2e31-47eb-8c8d-822c11b04a07 · outbound

This paper cites Takeda, Finiteness of trivial solutions of factorial products yielding a factorial over number fields.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Takeda, Finiteness of trivial solutions of factorial products yielding a factorial over number fields

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.481250Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:7611ceb8fe5416baaf935e70f840c52921f8a86ec25da52932c4d64115ea958c

Observation 8ffad563-e6f4-4bf8-9fe1-70a48e275889 · outbound

This paper cites Takeda, On the finiteness of solutions for polynomial-factorial Diophantine equations.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Takeda, On the finiteness of solutions for polynomial-factorial Diophantine equations

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.442350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:7b1fcfbaab39b8b43a7e1f47dbd74f266b8038c6240da6987835027d4b498899

Observation 7c5beda0-431b-498f-95cd-2ffd0e6a60ef · outbound

This paper cites Takeda, Product of Factorials Equal Another Product of Factorials.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Takeda, Product of Factorials Equal Another Product of Factorials

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.454942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:f15e25adee5b1396ba549975f666f2d9df95a286781a83cd8bc30003a7261b0b

Observation b9fcf0d3-fdf7-4339-8d42-bf14170a801d · outbound

This paper cites Siegel: Aproximation algebraischer Zahlen.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Siegel: Aproximation algebraischer Zahlen

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.419400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:0ffbb6a1c933fe407789815a587438bf371bc99a6b81d08c86041427ab823d3e

Observation 2a78e327-4989-45a4-ba4a-73967623aa03 · outbound

This paper cites Tijdeman: Applications of the Gel'fond--Baker method to rational number theory.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Tijdeman: Applications of the Gel'fond--Baker method to rational number theory

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.431968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:cebc8d973a69de11ab5fc9f6c981b384ba28fd3ddea5351e335fbcd983563b62

Observation 9f5388ef-4a2a-415b-ac6d-427ccabc20ac · outbound

This paper cites Ulas, Some observations on the Diophantine equation y^2=x!+A and related results.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Ulas, Some observations on the Diophantine equation y^2=x!+A and related results

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.494963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:24dcb436256a3cdfcb6a9bcffc13748d4f1da7ba5067bb1e3b4d66271c8ddf68

Observation 91ea14e9-3f58-4ab4-9768-a06e3b6f3ec0 · outbound

This paper cites Ulas, Some experiments with Ramanujan--Nagell type Diophantine equations.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Ulas, Some experiments with Ramanujan--Nagell type Diophantine equations

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.497290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:27100b35279ebcb74efe06aea46477a1827e4b4346f3fcec1df43001b857e5fd

Observation 32b0a895-8007-4255-9eb2-0d8570803778 · outbound

This paper cites Yamada, A generalization of the Ramanujan--Nagell equation.

A comment on the equation $n!!=a_1!!\cdots a_t!!$ Yamada, A generalization of the Ramanujan--Nagell equation

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-05-17T06:01:35.435890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-05-10T18:17:05.380100Z digest=sha256:0ca1398123a9433f44b24ab678edd9c03f61c6cfc35d742a7b079555eb4fce2a

Pith citing papers

No inbound Pith citation observations are available.