{"paper":{"title":"Perfect powers in products of terms of elliptic divisibility sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lajos Hajdu, M\\'arton Szikszai, Shanta Laishram","submitted_at":"2016-04-13T09:48:02Z","abstract_excerpt":"Diophantine problems involving recurrence sequences have a long history and is an actively studied topic within number theory. In this paper, we connect to the field by considering the equation \\begin{align*} B_mB_{m+d}\\dots B_{m+(k-1)d}=y^\\ell \\end{align*} in positive integers $m,d,k,y$ with $\\gcd(m,d)=1$ and $k\\geq 2$, where $\\ell\\geq 2$ is a fixed integer and $B=(B_n)_{n=1}^\\infty$ is an elliptic divisibility sequence, an important class of non-linear recurrences. We prove that the above equation admits only finitely many solutions. In fact, we present an algorithm to find all possible solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03707","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"}