{"paper":{"title":"Non-extensibility of the pair $\\{1, 3\\}$ to a Diophantine quintuple in $\\mathbb{Z}\\left[\\sqrt{-d}\\right]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dijana Kreso, Zrinka Franu\\v{s}i\\'c","submitted_at":"2013-12-18T17:43:13Z","abstract_excerpt":"We show that the Diophantine pair $\\{1, 3\\}$ can not be extended to a Diophantine quintuple in $\\mathbb{Z}\\left[\\sqrt{-2}\\right]$. This result completes the work of the first author and establishes non-extensibility of the Diophantine pair $\\{1, 3\\}$ to a Diophantine quintuple in $\\mathbb{Z}\\left[\\sqrt{-d}\\right]$ for all $d\\in \\mathbb{N}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5241","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"}