{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UWZBVXCPXHDZGSTN56M6WSHEET","short_pith_number":"pith:UWZBVXCP","schema_version":"1.0","canonical_sha256":"a5b21adc4fb9c7934a6def99eb48e424ff3e4ffdaba7cddf1b40b5c1edcb84c0","source":{"kind":"arxiv","id":"1702.08500","version":1},"attestation_state":"computed","paper":{"title":"On the Diophantine equations X^3+Y^3+Z^3+aU^k=a_0U_0^{t_0}+...+a_nU_n^{t_n}, k=3,4","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Farzali Izadi, Mehdi Baghalaghdam","submitted_at":"2017-02-15T23:07:45Z","abstract_excerpt":"In this paper, elliptic curves theory is used for solving the Diophantine equations X^3+Y^3+Z^3+aU^k=a_0U_0^{t_0}+...+a_nU_n^{t_n}, k=3,4 where n, ti are natural numbers and a, a_i are fixed arbitrary rational numbers. We try to transform each case of the above Diophantine equations to a cubic elliptic curve of positive rank, then get infinitely many integer solutions for each case. We also solve these Diophantine equations for some values of n, a, a_i, t_i, and obtain infinitely many solutions for each case, and show among the other things that how sums of four, five, or more cubics can be wr"},"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":"1702.08500","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-15T23:07:45Z","cross_cats_sorted":[],"title_canon_sha256":"0c25cd0115d006bc09c398386ebb4e125a5f313abcb95309fe5c6da466378402","abstract_canon_sha256":"d1550afbf533dfff2cdc2ad9d56f8ea013c6ffc9d53e4e8829e74a2c2c1e7fb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:48.545914Z","signature_b64":"Uw1e2UuJqYlPj5ZksHK/AyLi6AsgHepBJ1MVAOtkUH0SnY1kcqGWoNB9Kw0gPyudMfDrdl5DM87gdP364O0DAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5b21adc4fb9c7934a6def99eb48e424ff3e4ffdaba7cddf1b40b5c1edcb84c0","last_reissued_at":"2026-05-18T00:49:48.545486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:48.545486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Diophantine equations X^3+Y^3+Z^3+aU^k=a_0U_0^{t_0}+...+a_nU_n^{t_n}, k=3,4","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Farzali Izadi, Mehdi Baghalaghdam","submitted_at":"2017-02-15T23:07:45Z","abstract_excerpt":"In this paper, elliptic curves theory is used for solving the Diophantine equations X^3+Y^3+Z^3+aU^k=a_0U_0^{t_0}+...+a_nU_n^{t_n}, k=3,4 where n, ti are natural numbers and a, a_i are fixed arbitrary rational numbers. We try to transform each case of the above Diophantine equations to a cubic elliptic curve of positive rank, then get infinitely many integer solutions for each case. We also solve these Diophantine equations for some values of n, a, a_i, t_i, and obtain infinitely many solutions for each case, and show among the other things that how sums of four, five, or more cubics can be wr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08500","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":"1702.08500","created_at":"2026-05-18T00:49:48.545558+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.08500v1","created_at":"2026-05-18T00:49:48.545558+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08500","created_at":"2026-05-18T00:49:48.545558+00:00"},{"alias_kind":"pith_short_12","alias_value":"UWZBVXCPXHDZ","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"UWZBVXCPXHDZGSTN","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"UWZBVXCP","created_at":"2026-05-18T12:31:49.984773+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/UWZBVXCPXHDZGSTN56M6WSHEET","json":"https://pith.science/pith/UWZBVXCPXHDZGSTN56M6WSHEET.json","graph_json":"https://pith.science/api/pith-number/UWZBVXCPXHDZGSTN56M6WSHEET/graph.json","events_json":"https://pith.science/api/pith-number/UWZBVXCPXHDZGSTN56M6WSHEET/events.json","paper":"https://pith.science/paper/UWZBVXCP"},"agent_actions":{"view_html":"https://pith.science/pith/UWZBVXCPXHDZGSTN56M6WSHEET","download_json":"https://pith.science/pith/UWZBVXCPXHDZGSTN56M6WSHEET.json","view_paper":"https://pith.science/paper/UWZBVXCP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.08500&json=true","fetch_graph":"https://pith.science/api/pith-number/UWZBVXCPXHDZGSTN56M6WSHEET/graph.json","fetch_events":"https://pith.science/api/pith-number/UWZBVXCPXHDZGSTN56M6WSHEET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UWZBVXCPXHDZGSTN56M6WSHEET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UWZBVXCPXHDZGSTN56M6WSHEET/action/storage_attestation","attest_author":"https://pith.science/pith/UWZBVXCPXHDZGSTN56M6WSHEET/action/author_attestation","sign_citation":"https://pith.science/pith/UWZBVXCPXHDZGSTN56M6WSHEET/action/citation_signature","submit_replication":"https://pith.science/pith/UWZBVXCPXHDZGSTN56M6WSHEET/action/replication_record"}},"created_at":"2026-05-18T00:49:48.545558+00:00","updated_at":"2026-05-18T00:49:48.545558+00:00"}