{"paper":{"title":"A note on $p$-adic valuations of the Schenker sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Piotr Miska","submitted_at":"2014-01-08T15:02:51Z","abstract_excerpt":"A prime number $p$ is called a Schenker prime if there exists such $n\\in\\mathbb{N}_+$ that $p\\nmid n$ and $p\\mid a_n$, where $a_n = \\sum_{j=0}^{n}\\frac{n!}{j!}n^j$ is so-called Schenker sum. T. Amdeberhan, D. Callan and V. Moll formulated two conjectures concerning $p$-adic valuations of $a_n$ in case when $p$ is a Schenker prime. In particular, they asked whether for each $k\\in\\mathbb{N}_+$ there exists the unique positive integer $n_k<p^k$ such that $v_p(a_{m\\cdot 5^k + n_k})\\geq k$ for each nonnegative integer $m$. We prove that for every $k\\in\\mathbb{N}_+$ the inequality $v_5(a_n)\\geq k$ h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1717","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"}