{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OMTOI6GSPTER5M455EFXVIPH6J","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":"7bb9e37165eec4565d347bd17205ca6df8fce33c33d29104fde63d3f63bc57ad","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-02-16T07:00:22Z","title_canon_sha256":"0f26ff59ab5f720b87431763eb30b6756043fb17260e8e80194e9a44e6fa16ef"},"schema_version":"1.0","source":{"id":"2102.07977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.07977","created_at":"2026-07-05T02:15:45Z"},{"alias_kind":"arxiv_version","alias_value":"2102.07977v1","created_at":"2026-07-05T02:15:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.07977","created_at":"2026-07-05T02:15:45Z"},{"alias_kind":"pith_short_12","alias_value":"OMTOI6GSPTER","created_at":"2026-07-05T02:15:45Z"},{"alias_kind":"pith_short_16","alias_value":"OMTOI6GSPTER5M45","created_at":"2026-07-05T02:15:45Z"},{"alias_kind":"pith_short_8","alias_value":"OMTOI6GS","created_at":"2026-07-05T02:15:45Z"}],"graph_snapshots":[{"event_id":"sha256:6b7c8f1b60ea14986f920c60bdf7e0d49fd4593a98c1de56236f14ec6ca19019","target":"graph","created_at":"2026-07-05T02:15:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.07977/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $c$ be a square-free positive integer and $p$ a prime satisfying $p\\nmid c$. Let $h(-c)$ denote the class number of the imaginary quadratic field $\\mathbb{Q}(\\sqrt{-c})$. In this paper, we consider the Diophantine equation $$cx^2+p^{2m}=4y^n,~~x,y\\geq 1, m\\geq 0, n\\geq 3, \\gcd(x,y)=1, \\gcd(n,2h(-c))=1,$$ and we describe all its integer solutions. Our main tool here is the prominent result of Bilu, Hanrot and Voutier on existence of primitive divisors in Lehmer sequences.","authors_text":"Azizul Hoque, Kalyan Chakraborty, Kotyada Srinivas","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-02-16T07:00:22Z","title":"On the Diophantine equation $cx^2+p^{2m}=4y^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.07977","kind":"arxiv","version":1},"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:d32f971044c5600025d4ef152021e20231fcec6fba050b5f1aad23b2be081f12","target":"record","created_at":"2026-07-05T02:15:45Z","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":"7bb9e37165eec4565d347bd17205ca6df8fce33c33d29104fde63d3f63bc57ad","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-02-16T07:00:22Z","title_canon_sha256":"0f26ff59ab5f720b87431763eb30b6756043fb17260e8e80194e9a44e6fa16ef"},"schema_version":"1.0","source":{"id":"2102.07977","kind":"arxiv","version":1}},"canonical_sha256":"7326e478d27cc91eb39de90b7aa1e7f25af26ee8b8e4470010972b481575c33b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7326e478d27cc91eb39de90b7aa1e7f25af26ee8b8e4470010972b481575c33b","first_computed_at":"2026-07-05T02:15:45.066356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:15:45.066356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5JlKadQSGEDCOuzEJK3fQtCIzULTtdWjR+qLm5BuFtODK87Z0wo5NFOfLvfaR03c7QVZ4RZZL6r2Z28R/LqnAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:15:45.066733Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.07977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d32f971044c5600025d4ef152021e20231fcec6fba050b5f1aad23b2be081f12","sha256:6b7c8f1b60ea14986f920c60bdf7e0d49fd4593a98c1de56236f14ec6ca19019"],"state_sha256":"a02dfd674890c59c045ecdf4eade097e7b156bfa042002d93874fc8e1d4c41e4"}