{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:654HUH26W2QVPHXC3D7U4ABD3T","short_pith_number":"pith:654HUH26","schema_version":"1.0","canonical_sha256":"f7787a1f5eb6a1579ee2d8ff4e0023dced7c7187335c254620e8a28179d69590","source":{"kind":"arxiv","id":"1602.08698","version":1},"attestation_state":"computed","paper":{"title":"Equal Sums of Like Powers with Minimum Number of Terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ajai Choudhry","submitted_at":"2016-02-28T10:39:52Z","abstract_excerpt":"This paper is concerned with the diophantine system, $\\sum_{i=1}^{s_1} x_i^r=\\sum_{i=1}^{s_2} y_i^r,\\, r=1,\\,2,\\,\\ldots,\\,k, $ where $s_1$ and $s_2$ are integers such that the total number of terms on both sides, that is, $s_1+s_2,$ is as small as possible. We define $\\beta(k)$ to be the minimum value of $s_1+s_2$ for which there exists a nontrivial solution of this diophantine system. We find nontrivial integer solutions of this diophantine system when $k < 6$, and thereby show that $\\beta(2) =4,\\;\\, \\beta(3) = 6,\\;\\, 7 \\leq \\beta(4) \\leq 8$ and $8 \\leq \\beta(5) \\leq 10$."},"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":"1602.08698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-28T10:39:52Z","cross_cats_sorted":[],"title_canon_sha256":"983b40098f91553cc4fb05b46ceb5ea497562299829820c1ce8fa256d318245b","abstract_canon_sha256":"0de65973374c19aa8f73d2bd586ee1f26f2ca401a19e9c77e1eac2ae8f10979c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:52.158081Z","signature_b64":"TmW39kDXlNdxW9JbzWr3LH19fb4we3x1N6R3Sf7gYnL6WZxjRRZCwK7kcx2X+RSsLcZpTJBnDaEMzT1RZi99Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7787a1f5eb6a1579ee2d8ff4e0023dced7c7187335c254620e8a28179d69590","last_reissued_at":"2026-05-18T01:19:52.157578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:52.157578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equal Sums of Like Powers with Minimum Number of Terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ajai Choudhry","submitted_at":"2016-02-28T10:39:52Z","abstract_excerpt":"This paper is concerned with the diophantine system, $\\sum_{i=1}^{s_1} x_i^r=\\sum_{i=1}^{s_2} y_i^r,\\, r=1,\\,2,\\,\\ldots,\\,k, $ where $s_1$ and $s_2$ are integers such that the total number of terms on both sides, that is, $s_1+s_2,$ is as small as possible. We define $\\beta(k)$ to be the minimum value of $s_1+s_2$ for which there exists a nontrivial solution of this diophantine system. We find nontrivial integer solutions of this diophantine system when $k < 6$, and thereby show that $\\beta(2) =4,\\;\\, \\beta(3) = 6,\\;\\, 7 \\leq \\beta(4) \\leq 8$ and $8 \\leq \\beta(5) \\leq 10$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08698","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":"1602.08698","created_at":"2026-05-18T01:19:52.157646+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.08698v1","created_at":"2026-05-18T01:19:52.157646+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08698","created_at":"2026-05-18T01:19:52.157646+00:00"},{"alias_kind":"pith_short_12","alias_value":"654HUH26W2QV","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"654HUH26W2QVPHXC","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"654HUH26","created_at":"2026-05-18T12:30:01.593930+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/654HUH26W2QVPHXC3D7U4ABD3T","json":"https://pith.science/pith/654HUH26W2QVPHXC3D7U4ABD3T.json","graph_json":"https://pith.science/api/pith-number/654HUH26W2QVPHXC3D7U4ABD3T/graph.json","events_json":"https://pith.science/api/pith-number/654HUH26W2QVPHXC3D7U4ABD3T/events.json","paper":"https://pith.science/paper/654HUH26"},"agent_actions":{"view_html":"https://pith.science/pith/654HUH26W2QVPHXC3D7U4ABD3T","download_json":"https://pith.science/pith/654HUH26W2QVPHXC3D7U4ABD3T.json","view_paper":"https://pith.science/paper/654HUH26","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.08698&json=true","fetch_graph":"https://pith.science/api/pith-number/654HUH26W2QVPHXC3D7U4ABD3T/graph.json","fetch_events":"https://pith.science/api/pith-number/654HUH26W2QVPHXC3D7U4ABD3T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/654HUH26W2QVPHXC3D7U4ABD3T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/654HUH26W2QVPHXC3D7U4ABD3T/action/storage_attestation","attest_author":"https://pith.science/pith/654HUH26W2QVPHXC3D7U4ABD3T/action/author_attestation","sign_citation":"https://pith.science/pith/654HUH26W2QVPHXC3D7U4ABD3T/action/citation_signature","submit_replication":"https://pith.science/pith/654HUH26W2QVPHXC3D7U4ABD3T/action/replication_record"}},"created_at":"2026-05-18T01:19:52.157646+00:00","updated_at":"2026-05-18T01:19:52.157646+00:00"}