{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H2HOZRIMSYEYMVS2RJG6SUKEG2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"34e1842cf9048f3a42a8b19ab287b106082b547c3df849a146f9c1bb43d0752e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-10T05:31:54Z","title_canon_sha256":"ad797a6f2b75207c901dade6c1556deeb989d57bdade46954a677175cdddd6f2"},"schema_version":"1.0","source":{"id":"1610.02774","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02774","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02774v4","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02774","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"pith_short_12","alias_value":"H2HOZRIMSYEY","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H2HOZRIMSYEYMVS2","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H2HOZRIM","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:d0142d6bd31e3d0fbf21e47c002e2eb801e02d8bca38d36f83db4ce390fe5acb","target":"graph","created_at":"2026-05-18T00:41:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Eshita Mazumdar, S. S. Rout","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-10T05:31:54Z","title":"Prime powers in sums of terms of binary recurrence sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02774","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3a1d24a7a3ae6e419aa29ecee4c2d7a9a4d784503221753ebd67186a09571369","target":"record","created_at":"2026-05-18T00:41:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"34e1842cf9048f3a42a8b19ab287b106082b547c3df849a146f9c1bb43d0752e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-10T05:31:54Z","title_canon_sha256":"ad797a6f2b75207c901dade6c1556deeb989d57bdade46954a677175cdddd6f2"},"schema_version":"1.0","source":{"id":"1610.02774","kind":"arxiv","version":4}},"canonical_sha256":"3e8eecc50c960986565a8a4de9514436b6af41726585d42c2e9b4a106ba9dd10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e8eecc50c960986565a8a4de9514436b6af41726585d42c2e9b4a106ba9dd10","first_computed_at":"2026-05-18T00:41:07.823330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:07.823330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rb9wlsVrpFp0AjwsKgV6deqrmikxcY15C3eaotYJQAmzespcsR+Awt0IIm687QtMOFBucT3uHRhw/oNZV8vJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:07.823790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02774","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a1d24a7a3ae6e419aa29ecee4c2d7a9a4d784503221753ebd67186a09571369","sha256:d0142d6bd31e3d0fbf21e47c002e2eb801e02d8bca38d36f83db4ce390fe5acb"],"state_sha256":"3eb0254566a5c5f744ec239de022d3ef65f6fcc4ffe8a7996eee2f259ca5aebe"}