{"paper":{"title":"Greatest common divisors of iterates of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Liang-Chung Hsia, Thomas J. Tucker","submitted_at":"2016-11-13T11:09:13Z","abstract_excerpt":"Following work of Bugeaud, Corvaja, and Zannier for integers, Ailon and Rudnick prove that for any multiplicatively independent polynomials, $a, b \\in {\\mathbb C}[x]$, there is a polynomial $h$ such that for all $n$, we have\n  \\[ \\gcd(a^n - 1, b^n - 1) \\mid h\\] We prove a compositional analog of this theorem, namely that if $f, g \\in {\\mathbb C}[x]$ are nonconstant compositionally independent polynomials and $c(x) \\in {\\mathbb C}[x]$, then there are at most finitely many $\\lambda$ with the property that there is an $n$ such that $(x - \\lambda)$ divides $\\gcd(f^{\\circ n}(x) - c(x), g^{\\circ n}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04115","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"}