Pith Number

pith:PIIRQS7X

pith:2013:PIIRQS7X74SY4KZQZZTNHXWLRU

not attested not anchored not stored refs pending

On the divisibility of $a^n \pm b^n$ by powers of $n$

Salvatore Tringali

arxiv:1301.0131 v3 · 2013-01-01 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PIIRQS7X74SY4KZQZZTNHXWLRU}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:06:51.694387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a11184bf7ff258e2b30ce66d3decb8d2a551f4693a3878f9d6dd8c42e7ea65a

Aliases

arxiv: 1301.0131 · arxiv_version: 1301.0131v3 · doi: 10.48550/arxiv.1301.0131 · pith_short_12: PIIRQS7X74SY · pith_short_16: PIIRQS7X74SY4KZQ · pith_short_8: PIIRQS7X

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PIIRQS7X74SY4KZQZZTNHXWLRU \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7a11184bf7ff258e2b30ce66d3decb8d2a551f4693a3878f9d6dd8c42e7ea65a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ff4ee435048a09e12a9d1f29876bfffb314d16e6558c48d7c0f09926e736334",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-01-01T20:16:27Z",
    "title_canon_sha256": "52f71a4ed5ee2942f3b046bd9d855e7e1c5b3627c2ff73a31aa3192d5edd3a67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.0131",
    "kind": "arxiv",
    "version": 3
  }
}