{"paper":{"title":"Distribution of factorials modulo p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Marc Munsch, Oleksiy Klurman","submitted_at":"2015-05-05T21:59:20Z","abstract_excerpt":"We prove that the sequence $n!\\,(\\bmod\\,p)$ occupies at least $\\sqrt{\\frac{3}{2}N}$ residue classes in the short interval $H\\le n \\le H+N$ and $N\\gg p^{\\frac{1}{4}}$ improving previously known trivial bound $\\sqrt{N}.$ In the other direction, we estimate the average number of residue classes missed by the sequence $n!\\,(\\bmod\\,p)$ for $p\\le x.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01198","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"}