{"paper":{"title":"A symmetric diophantine equation involving biquadrates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ajai Choudhry","submitted_at":"2017-02-14T03:09:53Z","abstract_excerpt":"This paper is concerned with the diophantine equation $\\sum_{i=1}^na_ix_i^4= \\sum_{i=1}^na_iy_i^4$ where $n \\geq 3$ and $a_i,\\,i=1,\\,2,\\,\\ldots,\\,n$, are arbitrary integers. While a method of obtaining numerical solutions of such an equation has recently been given, it seems that an explicit parametric of this diophantine equation has not yet been published. We obtain a multi-parameter solution of this equation for arbitrary values of $a_i$ and for any positive integer $n \\geq 3$, and deduce specific solutions when $n=3$ and $n=4$. The numerical solutions thus obtained are much smaller than th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04056","kind":"arxiv","version":2},"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"}