{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ERJEVIBWLHTTQD2YZTYKLV7CYN","short_pith_number":"pith:ERJEVIBW","schema_version":"1.0","canonical_sha256":"24524aa03659e7380f58ccf0a5d7e2c35901bbd734326f4aa951d4bf7c3ce1ee","source":{"kind":"arxiv","id":"1309.7537","version":1},"attestation_state":"computed","paper":{"title":"A variety of Euler's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tianxin Cai, Yong Zhang","submitted_at":"2013-09-29T05:12:57Z","abstract_excerpt":"We consider a variety of Euler's conjecture, i.e., whether the Diophantine system \\[\\begin{cases} n=a_{1}+a_{2}+\\cdots+a_{s-1}, a_{1}a_{2}\\cdots a_{s-1}(a_{1}+a_{2}+\\cdots+a_{s-1})=b^{s} \\end{cases}\\] has solutions $n,b,a_i\\in\\mathbb{Z}^+,i=1,2,\\ldots,s-1,s\\geq 3.$ By using the theory of elliptic curves, we prove that it has no solutions $n,b,a_i\\in\\mathbb{Z}^+$ for $s=3$, but for $s=4$ it has infinitely many solutions $n,b,a_i\\in\\mathbb{Z}^+$ and for $s\\geq 5$ there are infinitely many polynomial solutions $n,b,a_i\\in\\mathbb{Z}[t_1,t_2,\\ldots,t_{s-3}]$ with positive value satisfying this Diop"},"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":"1309.7537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-29T05:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"2e5848052dbebe34255efe2fc458e36b760396d73ebca14f287a6fc4dab20eda","abstract_canon_sha256":"feb2243b795215de95b75cd1d65a65f8996cf34e5a60c1aaacc0e7c21444fa3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:56.669070Z","signature_b64":"KHnqnw7xbeT9HhsqHhBF/3EYdPgBQ0+TFcv0lcxjTNPtb9/q8auuP5NWiiyHGPwOVS30jtLwhYs1XBUXccGrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24524aa03659e7380f58ccf0a5d7e2c35901bbd734326f4aa951d4bf7c3ce1ee","last_reissued_at":"2026-05-18T03:11:56.668339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:56.668339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A variety of Euler's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tianxin Cai, Yong Zhang","submitted_at":"2013-09-29T05:12:57Z","abstract_excerpt":"We consider a variety of Euler's conjecture, i.e., whether the Diophantine system \\[\\begin{cases} n=a_{1}+a_{2}+\\cdots+a_{s-1}, a_{1}a_{2}\\cdots a_{s-1}(a_{1}+a_{2}+\\cdots+a_{s-1})=b^{s} \\end{cases}\\] has solutions $n,b,a_i\\in\\mathbb{Z}^+,i=1,2,\\ldots,s-1,s\\geq 3.$ By using the theory of elliptic curves, we prove that it has no solutions $n,b,a_i\\in\\mathbb{Z}^+$ for $s=3$, but for $s=4$ it has infinitely many solutions $n,b,a_i\\in\\mathbb{Z}^+$ and for $s\\geq 5$ there are infinitely many polynomial solutions $n,b,a_i\\in\\mathbb{Z}[t_1,t_2,\\ldots,t_{s-3}]$ with positive value satisfying this Diop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7537","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":"1309.7537","created_at":"2026-05-18T03:11:56.668453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.7537v1","created_at":"2026-05-18T03:11:56.668453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7537","created_at":"2026-05-18T03:11:56.668453+00:00"},{"alias_kind":"pith_short_12","alias_value":"ERJEVIBWLHTT","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"ERJEVIBWLHTTQD2Y","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"ERJEVIBW","created_at":"2026-05-18T12:27:43.054852+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/ERJEVIBWLHTTQD2YZTYKLV7CYN","json":"https://pith.science/pith/ERJEVIBWLHTTQD2YZTYKLV7CYN.json","graph_json":"https://pith.science/api/pith-number/ERJEVIBWLHTTQD2YZTYKLV7CYN/graph.json","events_json":"https://pith.science/api/pith-number/ERJEVIBWLHTTQD2YZTYKLV7CYN/events.json","paper":"https://pith.science/paper/ERJEVIBW"},"agent_actions":{"view_html":"https://pith.science/pith/ERJEVIBWLHTTQD2YZTYKLV7CYN","download_json":"https://pith.science/pith/ERJEVIBWLHTTQD2YZTYKLV7CYN.json","view_paper":"https://pith.science/paper/ERJEVIBW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.7537&json=true","fetch_graph":"https://pith.science/api/pith-number/ERJEVIBWLHTTQD2YZTYKLV7CYN/graph.json","fetch_events":"https://pith.science/api/pith-number/ERJEVIBWLHTTQD2YZTYKLV7CYN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ERJEVIBWLHTTQD2YZTYKLV7CYN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ERJEVIBWLHTTQD2YZTYKLV7CYN/action/storage_attestation","attest_author":"https://pith.science/pith/ERJEVIBWLHTTQD2YZTYKLV7CYN/action/author_attestation","sign_citation":"https://pith.science/pith/ERJEVIBWLHTTQD2YZTYKLV7CYN/action/citation_signature","submit_replication":"https://pith.science/pith/ERJEVIBWLHTTQD2YZTYKLV7CYN/action/replication_record"}},"created_at":"2026-05-18T03:11:56.668453+00:00","updated_at":"2026-05-18T03:11:56.668453+00:00"}