{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SOXYUTQ77MLAIOROPWYS4SXKOI","short_pith_number":"pith:SOXYUTQ7","schema_version":"1.0","canonical_sha256":"93af8a4e1ffb16043a2e7db12e4aea722e2c75f085a8b3119b5d8a332d4604b3","source":{"kind":"arxiv","id":"1512.02817","version":1},"attestation_state":"computed","paper":{"title":"On decompositions of quadrinomials and related Diophantine equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maciej Gawron","submitted_at":"2015-12-09T11:28:19Z","abstract_excerpt":"Let $A,B,C,D$ be rational numbers such that $ABC \\neq 0$, and let $n_1>n_2>n_3>0$ be positive integers. We solve the equation\n  $$ Ax^{n_1}+Bx^{n_2}+Cx^{n_3}+D = f(g(x)),$$ in $f,g \\in \\mathbb{Q}[x]$. In sequel we use Bilu-Tichy method to prove finitness of integral solutions of the equations $$ Ax^{n_1}+Bx^{n_2}+Cx^{n_3}+D = Ey^{m_1}+Fy^{m_2}+Gy^{m_3}+H, $$ where $A,B,C,D,E,F,G,H$ are rational numbers $ABCEFG \\neq 0$ and $n_1>n_2>n_3>0$, $m_1>m_2>m_3>0$, $\\gcd(n_1,n_2,n_3) = \\gcd(m_1,m_2,m_3)=1$ and $n_1,m_1 \\geq 9$. And the equation $$ A_1x^{n_1}+A_2x^{n_2}+\\ldots+A_l x^{n_l} + A_{l+1} = Ey^"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.02817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-09T11:28:19Z","cross_cats_sorted":[],"title_canon_sha256":"04be8fa8b31bc6956bc55c64413bf1088165bdb8e413ca0232a09fc6b82c6ae2","abstract_canon_sha256":"670578f63939cd740b3665fb6c448a02ef4a31d0cfa2d6b47cbf34f03af5b40d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:43.103774Z","signature_b64":"2r0QbdUobFbyAU4rMaOdvcfFzojMf6TuuEWBnmyI4CY/Lu07Cmv/jbA5P6fjg729/QZXyOD5d72IxB+XyE39DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93af8a4e1ffb16043a2e7db12e4aea722e2c75f085a8b3119b5d8a332d4604b3","last_reissued_at":"2026-05-18T01:24:43.103434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:43.103434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On decompositions of quadrinomials and related Diophantine equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maciej Gawron","submitted_at":"2015-12-09T11:28:19Z","abstract_excerpt":"Let $A,B,C,D$ be rational numbers such that $ABC \\neq 0$, and let $n_1>n_2>n_3>0$ be positive integers. We solve the equation\n  $$ Ax^{n_1}+Bx^{n_2}+Cx^{n_3}+D = f(g(x)),$$ in $f,g \\in \\mathbb{Q}[x]$. In sequel we use Bilu-Tichy method to prove finitness of integral solutions of the equations $$ Ax^{n_1}+Bx^{n_2}+Cx^{n_3}+D = Ey^{m_1}+Fy^{m_2}+Gy^{m_3}+H, $$ where $A,B,C,D,E,F,G,H$ are rational numbers $ABCEFG \\neq 0$ and $n_1>n_2>n_3>0$, $m_1>m_2>m_3>0$, $\\gcd(n_1,n_2,n_3) = \\gcd(m_1,m_2,m_3)=1$ and $n_1,m_1 \\geq 9$. And the equation $$ A_1x^{n_1}+A_2x^{n_2}+\\ldots+A_l x^{n_l} + A_{l+1} = Ey^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02817","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":"1512.02817","created_at":"2026-05-18T01:24:43.103490+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.02817v1","created_at":"2026-05-18T01:24:43.103490+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02817","created_at":"2026-05-18T01:24:43.103490+00:00"},{"alias_kind":"pith_short_12","alias_value":"SOXYUTQ77MLA","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SOXYUTQ77MLAIORO","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SOXYUTQ7","created_at":"2026-05-18T12:29:42.218222+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/SOXYUTQ77MLAIOROPWYS4SXKOI","json":"https://pith.science/pith/SOXYUTQ77MLAIOROPWYS4SXKOI.json","graph_json":"https://pith.science/api/pith-number/SOXYUTQ77MLAIOROPWYS4SXKOI/graph.json","events_json":"https://pith.science/api/pith-number/SOXYUTQ77MLAIOROPWYS4SXKOI/events.json","paper":"https://pith.science/paper/SOXYUTQ7"},"agent_actions":{"view_html":"https://pith.science/pith/SOXYUTQ77MLAIOROPWYS4SXKOI","download_json":"https://pith.science/pith/SOXYUTQ77MLAIOROPWYS4SXKOI.json","view_paper":"https://pith.science/paper/SOXYUTQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.02817&json=true","fetch_graph":"https://pith.science/api/pith-number/SOXYUTQ77MLAIOROPWYS4SXKOI/graph.json","fetch_events":"https://pith.science/api/pith-number/SOXYUTQ77MLAIOROPWYS4SXKOI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SOXYUTQ77MLAIOROPWYS4SXKOI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SOXYUTQ77MLAIOROPWYS4SXKOI/action/storage_attestation","attest_author":"https://pith.science/pith/SOXYUTQ77MLAIOROPWYS4SXKOI/action/author_attestation","sign_citation":"https://pith.science/pith/SOXYUTQ77MLAIOROPWYS4SXKOI/action/citation_signature","submit_replication":"https://pith.science/pith/SOXYUTQ77MLAIOROPWYS4SXKOI/action/replication_record"}},"created_at":"2026-05-18T01:24:43.103490+00:00","updated_at":"2026-05-18T01:24:43.103490+00:00"}