{"paper":{"title":"Periodicity in the $p$-adic valuation of a polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eric Rowland, Luis A. Medina, Victor H. Moll","submitted_at":"2015-05-09T18:35:48Z","abstract_excerpt":"For a prime $p$ and an integer $x$, the $p$-adic valuation of $x$ is denoted by $\\nu_{p}(x)$. For a polynomial $Q$ with integer coefficients, the sequence of valuations $\\nu_{p}(Q(n))$ is shown to be either periodic or unbounded. The first case corresponds to the situation where $Q$ has no roots in the ring of $p$-adic integers. In the periodic situation, the period length is determined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02302","kind":"arxiv","version":2},"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"}