{"paper":{"title":"$S$-parts of terms of integer linear recurrence sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jan-Hendrik Evertse, Yann Bugeaud","submitted_at":"2016-11-02T07:14:17Z","abstract_excerpt":"Let $S = \\{q_1, \\ldots , q_s\\}$ be a finite, non-empty set of distinct prime numbers. For a non-zero integer $m$, write $m = q_1^{r_1} \\ldots q_s^{r_s} M$, where $r_1, \\ldots , r_s$ are non-negative integers and $M$ is an integer relatively prime to $q_1 \\ldots q_s$. We define the $S$-part $[m]_S$ of $m$ by $[m]_S := q_1^{r_1} \\ldots q_s^{r_s}$. Let $(u_n)_{n \\ge 0}$ be a linear recurrence sequence of integers. Under certain necessary conditions, we establish that for every $\\varepsilon > 0$, there exists an integer $n_0$ such that $[u_n]_S\\leq |u_n|^{\\varepsilon}$ holds for $n > n_0$. Our pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00485","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"}