{"paper":{"title":"On the Diophantine equation $cx^2+p^{2m}=4y^n$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Azizul Hoque, Kalyan Chakraborty, Kotyada Srinivas","submitted_at":"2021-02-16T07:00:22Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.07977","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.07977/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}