{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IBQ5UVPUUNZ4SFKZ6LXADAQUDF","short_pith_number":"pith:IBQ5UVPU","schema_version":"1.0","canonical_sha256":"4061da55f4a373c91559f2ee018214194369c4fd78624c340fcfcde356cd313d","source":{"kind":"arxiv","id":"1607.06366","version":3},"attestation_state":"computed","paper":{"title":"On the equation $ \\boldsymbol{n_1n_2=n_3n_4}$ restricted to factor closed sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michel Weber, Sanying Shi","submitted_at":"2016-07-21T15:37:27Z","abstract_excerpt":"We study the number of solutions $N(B,F)$ of the diophantine equation $n_1n_2=n_3n_4$, where $1\\le n_1\\le B$, $1\\le n_3\\le B$, $n_2, n_4\\in F$ and $F\\subset [1,B]$ is a factor closed set. We study more particularly the case when $F= \\big\\{m=p_1^{\\e_1}\\ldots p_k^{\\e_k}, \\e_j\\in \\{0,1\\}, 1\\le j\\le k\\big\\}$,\n  $p_1,\\ldots,p_k$ being distinct prime numbers."},"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":"1607.06366","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-21T15:37:27Z","cross_cats_sorted":[],"title_canon_sha256":"723f09c5873d9acd8981bf62349f234734f0f585eb5756ca2544971d749eb86c","abstract_canon_sha256":"3bd3c8e79a44a11f2b82e6a700a3972377a34319be2537cc0bbea744c6835b33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:32.770471Z","signature_b64":"1pmXlsNrE+KyJKA1imJPCoZ6TOpOTXsZYc2rXwKmC7WDbq/4sVOqhiHkI3BICcoev+PZnmqKZxPOLF9WsLpXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4061da55f4a373c91559f2ee018214194369c4fd78624c340fcfcde356cd313d","last_reissued_at":"2026-05-18T00:04:32.769957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:32.769957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the equation $ \\boldsymbol{n_1n_2=n_3n_4}$ restricted to factor closed sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michel Weber, Sanying Shi","submitted_at":"2016-07-21T15:37:27Z","abstract_excerpt":"We study the number of solutions $N(B,F)$ of the diophantine equation $n_1n_2=n_3n_4$, where $1\\le n_1\\le B$, $1\\le n_3\\le B$, $n_2, n_4\\in F$ and $F\\subset [1,B]$ is a factor closed set. We study more particularly the case when $F= \\big\\{m=p_1^{\\e_1}\\ldots p_k^{\\e_k}, \\e_j\\in \\{0,1\\}, 1\\le j\\le k\\big\\}$,\n  $p_1,\\ldots,p_k$ being distinct prime numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06366","kind":"arxiv","version":3},"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":"1607.06366","created_at":"2026-05-18T00:04:32.770042+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.06366v3","created_at":"2026-05-18T00:04:32.770042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06366","created_at":"2026-05-18T00:04:32.770042+00:00"},{"alias_kind":"pith_short_12","alias_value":"IBQ5UVPUUNZ4","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IBQ5UVPUUNZ4SFKZ","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IBQ5UVPU","created_at":"2026-05-18T12:30:22.444734+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/IBQ5UVPUUNZ4SFKZ6LXADAQUDF","json":"https://pith.science/pith/IBQ5UVPUUNZ4SFKZ6LXADAQUDF.json","graph_json":"https://pith.science/api/pith-number/IBQ5UVPUUNZ4SFKZ6LXADAQUDF/graph.json","events_json":"https://pith.science/api/pith-number/IBQ5UVPUUNZ4SFKZ6LXADAQUDF/events.json","paper":"https://pith.science/paper/IBQ5UVPU"},"agent_actions":{"view_html":"https://pith.science/pith/IBQ5UVPUUNZ4SFKZ6LXADAQUDF","download_json":"https://pith.science/pith/IBQ5UVPUUNZ4SFKZ6LXADAQUDF.json","view_paper":"https://pith.science/paper/IBQ5UVPU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.06366&json=true","fetch_graph":"https://pith.science/api/pith-number/IBQ5UVPUUNZ4SFKZ6LXADAQUDF/graph.json","fetch_events":"https://pith.science/api/pith-number/IBQ5UVPUUNZ4SFKZ6LXADAQUDF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IBQ5UVPUUNZ4SFKZ6LXADAQUDF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IBQ5UVPUUNZ4SFKZ6LXADAQUDF/action/storage_attestation","attest_author":"https://pith.science/pith/IBQ5UVPUUNZ4SFKZ6LXADAQUDF/action/author_attestation","sign_citation":"https://pith.science/pith/IBQ5UVPUUNZ4SFKZ6LXADAQUDF/action/citation_signature","submit_replication":"https://pith.science/pith/IBQ5UVPUUNZ4SFKZ6LXADAQUDF/action/replication_record"}},"created_at":"2026-05-18T00:04:32.770042+00:00","updated_at":"2026-05-18T00:04:32.770042+00:00"}