{"paper":{"title":"Cyclotomic Coincidences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carl Pomerance, Simon Rubinstein-Salzedo","submitted_at":"2019-03-05T18:11:40Z","abstract_excerpt":"In this paper, we show that if $m$ and $n$ are distinct positive integers and $x$ is a nonzero real number with $\\Phi_m(x)=\\Phi_n(x)$, then $\\frac{1}{2}<|x|<2$ except when $\\{m,n\\}=\\{2,6\\}$ and $x=2$. We also observe that 2 appears to be the largest limit point of the set of values of $x$ for which $\\Phi_m(x)=\\Phi_n(x)$ for some $m\\neq n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01962","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"}