{"paper":{"title":"On the Diophantine equation $\\binom{n}{k}=\\binom{m}{l}+d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Homero R. Gallegos-Ruiz, Maciej Ulas, Nikolaos Katsipis, Szabolcs Tengely","submitted_at":"2019-04-25T14:24:28Z","abstract_excerpt":"By finding all integral points on certain elliptic and hyperelliptic curves we completely solve the Diophantine equation $\\binom{n}{k}=\\binom{m}{l}+d$ for $-3\\leq d\\leq 3$ and $(k,l)\\in\\{(2,3),\\; (2,4),\\;(2,5),\\; (2,6),\\; (2,8),\\; (3,4),\\; (3,6),\\; (4,6), \\; (4,8)\\}.$ Moreover, we present some other observations of computational and theoretical nature concerning the title equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11369","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"}