{"paper":{"title":"On the Diophantine equation $(x+1)^{k}+(x+2)^{k}+...+(lx)^{k}=y^{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"G\\\"okhan Soydan","submitted_at":"2017-01-10T08:12:56Z","abstract_excerpt":"Let $k,l\\geq2$ be fixed integers. In this paper, firstly, we prove that all solutions of the equation $(x+1)^{k}+(x+2)^{k}+...+(lx)^{k}=y^{n}$ in integers $x,y,n$ with $x,y\\geq1, n\\geq2$ satisfy $n<C_{1}$ where $C_{1}=C_{1}(l,k)$ is an effectively computable constant. Secondly, we prove that all solutions of this equation in integers $x,y,n$ with $x,y\\geq1, n\\geq2, k\\neq3$ and $l\\equiv0 \\pmod 2$ satisfy $\\max\\{x,y,n\\}<C_{2}$ where $C_{2}$ is an effectively computable constant depending only on $k$ and $l$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02466","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"}