{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:HTE65B4LZBHV5VYXNY3SIKP2LJ","short_pith_number":"pith:HTE65B4L","schema_version":"1.0","canonical_sha256":"3cc9ee878bc84f5ed7176e372429fa5a6c972a1f3ab05de9ba772c3d80a1313d","source":{"kind":"arxiv","id":"1203.0018","version":1},"attestation_state":"computed","paper":{"title":"The Rational Number n/p as a sum of two unit fractions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Konstantine Zelator","submitted_at":"2012-02-29T21:11:08Z","abstract_excerpt":"In a 2011 paper published in the journal \"Asian Journal of Algebra\"(see reference[1]), the authors consider, among other equations,the diophantine equations 2xy=n(x+y) and 3xy=n(x+y). For the first equation, with n being an odd positive integer, they give the solution x=(n+1)/2, y=n(n+1)/2. For the second equation they present the particular solution, x=(n+1)/3,y=n(n+1)/3, where is n is a positive integer congruent to 2modulo3. If in the above equations we assume n to be prime, then these two equations become special cases of the diophantine equation, nxy=p(x+y) (1), with p being a prime and n"},"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":"1203.0018","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GM","submitted_at":"2012-02-29T21:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"14b086b5773c86e2d3b5aa9097b3c93c64491f3779b42f4053943f1cf6d60d83","abstract_canon_sha256":"47850345b19b9018159b11282d464f2110feff72da9a5489b0edb7e4c3ffddad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:03.418395Z","signature_b64":"DuGfb33f0AQk9YVh29ELoyP1MTarlGjqEYye2AwfzRi8H/pfNa9tSmPRj0btBP3Q0p5OKt9jiMN0rIqDI5GYCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cc9ee878bc84f5ed7176e372429fa5a6c972a1f3ab05de9ba772c3d80a1313d","last_reissued_at":"2026-05-18T04:01:03.417850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:03.417850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Rational Number n/p as a sum of two unit fractions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Konstantine Zelator","submitted_at":"2012-02-29T21:11:08Z","abstract_excerpt":"In a 2011 paper published in the journal \"Asian Journal of Algebra\"(see reference[1]), the authors consider, among other equations,the diophantine equations 2xy=n(x+y) and 3xy=n(x+y). For the first equation, with n being an odd positive integer, they give the solution x=(n+1)/2, y=n(n+1)/2. For the second equation they present the particular solution, x=(n+1)/3,y=n(n+1)/3, where is n is a positive integer congruent to 2modulo3. If in the above equations we assume n to be prime, then these two equations become special cases of the diophantine equation, nxy=p(x+y) (1), with p being a prime and n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0018","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1203.0018","created_at":"2026-05-18T04:01:03.417924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.0018v1","created_at":"2026-05-18T04:01:03.417924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0018","created_at":"2026-05-18T04:01:03.417924+00:00"},{"alias_kind":"pith_short_12","alias_value":"HTE65B4LZBHV","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"HTE65B4LZBHV5VYX","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"HTE65B4L","created_at":"2026-05-18T12:27:09.501522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HTE65B4LZBHV5VYXNY3SIKP2LJ","json":"https://pith.science/pith/HTE65B4LZBHV5VYXNY3SIKP2LJ.json","graph_json":"https://pith.science/api/pith-number/HTE65B4LZBHV5VYXNY3SIKP2LJ/graph.json","events_json":"https://pith.science/api/pith-number/HTE65B4LZBHV5VYXNY3SIKP2LJ/events.json","paper":"https://pith.science/paper/HTE65B4L"},"agent_actions":{"view_html":"https://pith.science/pith/HTE65B4LZBHV5VYXNY3SIKP2LJ","download_json":"https://pith.science/pith/HTE65B4LZBHV5VYXNY3SIKP2LJ.json","view_paper":"https://pith.science/paper/HTE65B4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.0018&json=true","fetch_graph":"https://pith.science/api/pith-number/HTE65B4LZBHV5VYXNY3SIKP2LJ/graph.json","fetch_events":"https://pith.science/api/pith-number/HTE65B4LZBHV5VYXNY3SIKP2LJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HTE65B4LZBHV5VYXNY3SIKP2LJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HTE65B4LZBHV5VYXNY3SIKP2LJ/action/storage_attestation","attest_author":"https://pith.science/pith/HTE65B4LZBHV5VYXNY3SIKP2LJ/action/author_attestation","sign_citation":"https://pith.science/pith/HTE65B4LZBHV5VYXNY3SIKP2LJ/action/citation_signature","submit_replication":"https://pith.science/pith/HTE65B4LZBHV5VYXNY3SIKP2LJ/action/replication_record"}},"created_at":"2026-05-18T04:01:03.417924+00:00","updated_at":"2026-05-18T04:01:03.417924+00:00"}