{"paper":{"title":"Characterizing congruence preserving functions $Z/nZ\\to Z/mZ$ via rational polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.NT","authors_text":"Irene Guessarian, Patrick Cegielski, Serge Grigorieff","submitted_at":"2015-05-30T15:52:32Z","abstract_excerpt":"We introduce a basis of rational polynomial-like functions $P_0,\\ldots,P_{n-1}$ for the free module of functions $Z/nZ\\to Z/mZ$. We then characterize the subfamily of congruence preserving functions as the set of linear combinations of the functions $lcm(k)\\,P_k$ where $lcm(k)$ is the least common multiple of $2,\\ldots,k$ (viewed in $Z/mZ$). As a consequence, when $n\\geq m$, the number of such functions is independent of $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00133","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"}