{"paper":{"title":"Index divisibility in the orbit of 0 for integral polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael T. Urbanski, T. Alden Gassert","submitted_at":"2017-09-25T23:31:32Z","abstract_excerpt":"Let $f(x) \\in \\bbz[x]$ and consider the index divisibility set $D = \\{n \\in \\bbn : n \\mid f^n(0)\\}$. We present a number of properties of $D$ in the case that $(f^n(0))_{n=1}^\\infty$ is a rigid divisibility sequence, generalizing a number of results of Chen, Stange, and the first author. We then study the polynomial $x^d + x^e + c \\in \\bbz[x]$, where $d > e \\ge 2$ and determine all cases where this map has a finite index divisibility set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08751","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"}