{"paper":{"title":"A characterization of Sophie Germain primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paolo Leonetti","submitted_at":"2013-05-04T08:02:40Z","abstract_excerpt":"Let $n\\ge 5$ be an odd integer. It is shown that $\\{1^{\\sigma(1)},\\ldots,n^{\\sigma(n)}\\}$ is a complete residue system modulo $n$ for some permutation $\\sigma$ of $\\{1,\\ldots,n\\}$ if and only if $\\frac{1}{2}(n-1)$ is a Sophie Germain prime. Partial results are obtained also for the case $n$ even."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0893","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"}