{"paper":{"title":"A generalization of the Goresky-Klapper conjecture, Part I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Badria Alsulmi, Chris Pinner, C.J. Richardson, Ian Thompson, Michael J. Mossinghoff, Todd Cochrane, Vincent Pigno","submitted_at":"2018-05-05T04:55:54Z","abstract_excerpt":"For a fixed integer $n\\geq 2,$ we show that a permutation of the least residues mod $p$ of the form $f(x)=Ax^k$ mod $p$ cannot map a residue class mod $n$ to just one residue class mod $n$ once $p$ is sufficiently large, other than the maps $f(x)=\\pm x$ mod $p$ when $n$ is even and $f(x)=\\pm x$ or $\\pm x^{(p+1)/2}$ mod $p$ when $n$ is odd."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01998","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"}