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Number Theory 10: (2014) 565--568], it was shown that the necessary condition $b \\mid (a_1 a_2-1)(a_1-a_2)$ for equality of two dedekind sums $s(a_1,b)$ and $s(a_2,b)$ given in [Jabuka, Robins and Wang, When are two Dedekind sums equal? Internat. J. Number Theory 7: (2011) 2197--2202] is equivalent to $12s(a_1,b)-12s(a_2,b) \\in \\mathbb{Z}$. In this note, we give a new proof of this result and then find two additional necessary and sufficient conditions for $12s(a_1,b)-12s(a_2,b) \\in 2\\mathbb{Z}, 4\\mathb"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.3225","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-14T09:07:16Z","cross_cats_sorted":[],"title_canon_sha256":"a18427493e8407b3346e182b52692ce683511be4e44df0648825ca8642fa9c72","abstract_canon_sha256":"bb92444a23fb7a537f691f6a2b3227c8132d140d1fc891aabb7d0009435084ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:45.873985Z","signature_b64":"6vC4SdyTkCUJyFB0TSbiqmlVIyhYnygPEtm65VYpnH5rgyPpIuyKEk3zL/WUhOhpRV8DiVNFwIaFe8F9ANfNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"230179685a97e50b5994cba324e8734507029aeae97bae3466dde23f78e8dced","last_reissued_at":"2026-05-18T02:32:45.873353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:45.873353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equality of Dedekind sums mod $\\mathbb{Z},2\\mathbb{Z}$ and $4\\mathbb{Z}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Emmanuel Tsukerman","submitted_at":"2014-08-14T09:07:16Z","abstract_excerpt":"In [Girstmair, A criterion for the equality of Dedekind sums mod $\\mathbb{Z}$, Internat. 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