{"paper":{"title":"Primes $p \\equiv 1 \\bmod{d}$ and $a^{(p-1)/d} \\equiv 1 \\bmod{p}$}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liangyi Zhao, Peng Gao","submitted_at":"2018-07-25T01:46:23Z","abstract_excerpt":"Suppose that $d \\in \\{ 2, 3, 4, 6 \\}$ and $a \\in \\mathbb{Z}$ with $a\\neq -1$ and $a$ is not square. Let $P_{(a,d)}$ be the number of primes $p$ not exceeding $x$ such that $p \\equiv 1 \\pmod{d}$ and $a^{(p-1)/d} \\equiv 1 \\pmod{p}$. In this paper, we study the mean value of $P_{(a,d)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09410","kind":"arxiv","version":3},"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"}