{"paper":{"title":"The number of representations by a ternary sum of triangular numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Byeong-Kweon Oh, Mingyu Kim","submitted_at":"2018-01-15T15:05:44Z","abstract_excerpt":"For positive integers $a,b,c$, and an integer $n$, the number of integer solutions $(x,y,z) \\in \\mathbb Z^3$ of $a \\frac{x(x-1)}{2} + b \\frac{y(y-1)}{2} + c \\frac{z(z-1)}{2} = n$ is denoted by $t(a,b,c;n)$. In this article, we prove some relations between $t(a,b,c;n)$ and the numbers of representations of integers by some ternary quadratic forms. In particular, we prove various conjectures given by Z. H. Sun in \\cite{s}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04836","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"}