{"paper":{"title":"On the period of the linear congruential and power generators","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C. Pomerance, P. Kurlberg","submitted_at":"2004-05-07T16:55:08Z","abstract_excerpt":"We consider the periods of the linear congruential and the power generators modulo $n$ and, for fixed choices of initial parameters, give lower bounds that hold for ``most'' $n$ when $n$ ranges over three different sets: the set of primes, the set of products of two primes (of similar size), and the set of all integers. For most $n$ in these sets, the period is at least $n^{1/2+\\epsilon(n)}$ for any monotone function $\\epsilon(n)$ tending to zero as $n$ tends to infinity. Assuming the Generalized Riemann Hypothesis, for most $n$ in these sets the period is greater than $n^{1-\\epsilon}$ for any"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405120","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"}