{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:H2HOZRIMSYEYMVS2RJG6SUKEG2","short_pith_number":"pith:H2HOZRIM","schema_version":"1.0","canonical_sha256":"3e8eecc50c960986565a8a4de9514436b6af41726585d42c2e9b4a106ba9dd10","source":{"kind":"arxiv","id":"1610.02774","version":4},"attestation_state":"computed","paper":{"title":"Prime powers in sums of terms of binary recurrence sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eshita Mazumdar, S. S. Rout","submitted_at":"2016-10-10T05:31:54Z","abstract_excerpt":"Let $\\{u_{n}\\}_{n \\geq 0}$ be a non-degenerate binary recurrence sequence with positive, square-free discriminant and $p$ be a fixed prime number. In this paper, we have shown the finiteness result for the solutions of the Diophantine equation $u_{n_{1}} + u_{n_{2}} + \\cdots + u_{n_{t}} = p^{z}$ with some conditions on $n_i $ for all $1\\leq i \\leq t$. Moreover, we explicitly find all the powers of three which are sums of three balancing numbers using the lower bounds for linear forms in logarithms. Further, we use a variant of Baker-Davenport reduction method in Diophantine approximation due t"},"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":"1610.02774","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-10T05:31:54Z","cross_cats_sorted":[],"title_canon_sha256":"ad797a6f2b75207c901dade6c1556deeb989d57bdade46954a677175cdddd6f2","abstract_canon_sha256":"34e1842cf9048f3a42a8b19ab287b106082b547c3df849a146f9c1bb43d0752e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:07.823790Z","signature_b64":"Rb9wlsVrpFp0AjwsKgV6deqrmikxcY15C3eaotYJQAmzespcsR+Awt0IIm687QtMOFBucT3uHRhw/oNZV8vJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e8eecc50c960986565a8a4de9514436b6af41726585d42c2e9b4a106ba9dd10","last_reissued_at":"2026-05-18T00:41:07.823330Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:07.823330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Prime powers in sums of terms of binary recurrence sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eshita Mazumdar, S. S. Rout","submitted_at":"2016-10-10T05:31:54Z","abstract_excerpt":"Let $\\{u_{n}\\}_{n \\geq 0}$ be a non-degenerate binary recurrence sequence with positive, square-free discriminant and $p$ be a fixed prime number. In this paper, we have shown the finiteness result for the solutions of the Diophantine equation $u_{n_{1}} + u_{n_{2}} + \\cdots + u_{n_{t}} = p^{z}$ with some conditions on $n_i $ for all $1\\leq i \\leq t$. Moreover, we explicitly find all the powers of three which are sums of three balancing numbers using the lower bounds for linear forms in logarithms. Further, we use a variant of Baker-Davenport reduction method in Diophantine approximation due t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02774","kind":"arxiv","version":4},"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":"1610.02774","created_at":"2026-05-18T00:41:07.823400+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.02774v4","created_at":"2026-05-18T00:41:07.823400+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02774","created_at":"2026-05-18T00:41:07.823400+00:00"},{"alias_kind":"pith_short_12","alias_value":"H2HOZRIMSYEY","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"H2HOZRIMSYEYMVS2","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"H2HOZRIM","created_at":"2026-05-18T12:30:19.053100+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/H2HOZRIMSYEYMVS2RJG6SUKEG2","json":"https://pith.science/pith/H2HOZRIMSYEYMVS2RJG6SUKEG2.json","graph_json":"https://pith.science/api/pith-number/H2HOZRIMSYEYMVS2RJG6SUKEG2/graph.json","events_json":"https://pith.science/api/pith-number/H2HOZRIMSYEYMVS2RJG6SUKEG2/events.json","paper":"https://pith.science/paper/H2HOZRIM"},"agent_actions":{"view_html":"https://pith.science/pith/H2HOZRIMSYEYMVS2RJG6SUKEG2","download_json":"https://pith.science/pith/H2HOZRIMSYEYMVS2RJG6SUKEG2.json","view_paper":"https://pith.science/paper/H2HOZRIM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.02774&json=true","fetch_graph":"https://pith.science/api/pith-number/H2HOZRIMSYEYMVS2RJG6SUKEG2/graph.json","fetch_events":"https://pith.science/api/pith-number/H2HOZRIMSYEYMVS2RJG6SUKEG2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H2HOZRIMSYEYMVS2RJG6SUKEG2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H2HOZRIMSYEYMVS2RJG6SUKEG2/action/storage_attestation","attest_author":"https://pith.science/pith/H2HOZRIMSYEYMVS2RJG6SUKEG2/action/author_attestation","sign_citation":"https://pith.science/pith/H2HOZRIMSYEYMVS2RJG6SUKEG2/action/citation_signature","submit_replication":"https://pith.science/pith/H2HOZRIMSYEYMVS2RJG6SUKEG2/action/replication_record"}},"created_at":"2026-05-18T00:41:07.823400+00:00","updated_at":"2026-05-18T00:41:07.823400+00:00"}