{"paper":{"title":"A generalization of Gauss' triangular theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Byeong-Kweon Oh, Jangwon Ju","submitted_at":"2017-01-11T13:55:09Z","abstract_excerpt":"A quadratic polynomial $\\Phi_{a,b,c}(x,y,z)=x(ax+1)+y(by+1)+z(cz+1)$ is called universal if the diophantine equation $\\Phi_{a,b,c}(x,y,z)=n$ has an integer solution $x,y,z$ for any non negative integer $n$. In this article, we show that if $(a,b,c)=(2,2,6), (2,3,5)$ or $(2,3,7)$, then $\\Phi_{a,b,c}( x,y,z)$ is universal. These were conjectured by Sun in \\cite {Sun}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02974","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"}