{"paper":{"title":"Squarefree polynomials with prescribed coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Amotz Oppenheim, Mark Shusterman","submitted_at":"2017-07-20T14:18:08Z","abstract_excerpt":"For nonempty subsets $S_0, \\dots, S_{n-1}$ of a (large enough) finite field $\\mathbb{F}$ satisfying $$|S_1|, \\dots, |S_{n-1}| > 2 \\quad \\mathrm{or} \\quad |S_1|,|S_{n-1}| > n - 1,$$ we show that there exist $a_0 \\in S_0, \\dots, a_{n-1} \\in S_{n-1}$ such that $$ T^n + a_{n-1}T^{n-1} + \\dots + a_1T + a_0 \\in \\mathbb{F}[T] $$ is a squarefree polynomial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06528","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"}