{"paper":{"title":"On some general solutions of the simple Pell equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Vladimir Pletser","submitted_at":"2015-01-24T15:23:21Z","abstract_excerpt":"Two theorems are demonstrated giving analytical expressions of the fundamental solutions of the Pell equation $X^{2}-DY^{2}=1$ found by the method of continued fractions for two squarefree polynomial expressions of radicands of Richaud-Degert type $D$ of the form $D=\\left(f\\left(u\\right)\\right)^{2}\\pm2^{\\alpha}n$, where $D$, $n>0$, $\\alpha\\geq0,\\in\\mathbb{Z}$, and $f\\left(u\\right)>0,\\in\\mathbb{Z}$, any polynomial function of $u\\in\\mathbb{Z}$ such that $f\\left(u\\right)\\equiv0\\left(mod\\,\\left(2^{\\alpha-1}n\\right)\\right)$ or $f\\left(u\\right)\\equiv\\left(2^{\\alpha-2}n\\right)\\left(mod\\,\\left(2^{\\alp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06051","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"}