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We also prove that if q>8 then N_{n+1}(q)/N_n(q) (n=1,2,3,...) is strictly increasing."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.1562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-04T19:53:43Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"51e9496929996bd7300c743edb097e6aa8f00eed7c9528363162f607d5ffcc9e","abstract_canon_sha256":"b408b88f2be2269b52983bf0c2a4cc5188a615df40e17159bb3f104f2fbaf987"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:17.686471Z","signature_b64":"U7mNNC5JP5HkDkhER/Rc6jcYqhUeNMbunA/k0zqBtavndg0wUKjP9w9ZquHb8MD97xX20A4HeE/OwX96l6xPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"327ebd55a967a92cd93d5b03b1930e2385f64be6254e70e522375a704483bf6b","last_reissued_at":"2026-05-18T03:43:17.685915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:17.685915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On irreducible polynomials over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Zhi-Wei Sun","submitted_at":"2012-10-04T19:53:43Z","abstract_excerpt":"For n=1,2,3,... let N_n(q) denote the number of monic irreducible polynomials over the finite field F_q. 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