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We also show the irreducible factors in the case when ${\\rm rad}(n)$ divides $q-1$ and ${\\rm gcd}(m, n)=1$. Finally, using this algorithm we split $x^n-1$ into irreducible factors, in the case when $n=2^mp^t$ and $q$ is a generator of the group $\\mathbb{Z}_{p^2}^*$."},"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":"1511.08918","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-28T18:35:05Z","cross_cats_sorted":[],"title_canon_sha256":"b1e7e67032604816805c99f6560d53036589841433426a41fa0dd421b6f56db5","abstract_canon_sha256":"58c144c42ac7b71105206db8548d8c1168f30449f684ff346377b9ff8b66b55b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:46.111866Z","signature_b64":"7KKccqzLYAjIWHe5G9plTDI5dXOdti6Ztkh4AAvVPIxX0F/Ev/cXG95eSa2aeegcm0abUXB0piIqiW9v/5z+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"172e7f491d89fa9e936ef98c10cc6f2b2a56549c6698b0a7413b2e34676d8edc","last_reissued_at":"2026-05-18T01:25:46.111176Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:46.111176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factoring polynomials of the form $f(x^n)\\in \\mathbb{F}_q[x]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"F.E. 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Finally, using this algorithm we split $x^n-1$ into irreducible factors, in the case when $n=2^mp^t$ and $q$ is a generator of the group $\\mathbb{Z}_{p^2}^*$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08918","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.08918","created_at":"2026-05-18T01:25:46.111278+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.08918v1","created_at":"2026-05-18T01:25:46.111278+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08918","created_at":"2026-05-18T01:25:46.111278+00:00"},{"alias_kind":"pith_short_12","alias_value":"C4XH6SI5RH5J","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"C4XH6SI5RH5J5E3O","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"C4XH6SI5","created_at":"2026-05-18T12:29:14.074870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C4XH6SI5RH5J5E3O7GGBBTDPFM","json":"https://pith.science/pith/C4XH6SI5RH5J5E3O7GGBBTDPFM.json","graph_json":"https://pith.science/api/pith-number/C4XH6SI5RH5J5E3O7GGBBTDPFM/graph.json","events_json":"https://pith.science/api/pith-number/C4XH6SI5RH5J5E3O7GGBBTDPFM/events.json","paper":"https://pith.science/paper/C4XH6SI5"},"agent_actions":{"view_html":"https://pith.science/pith/C4XH6SI5RH5J5E3O7GGBBTDPFM","download_json":"https://pith.science/pith/C4XH6SI5RH5J5E3O7GGBBTDPFM.json","view_paper":"https://pith.science/paper/C4XH6SI5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.08918&json=true","fetch_graph":"https://pith.science/api/pith-number/C4XH6SI5RH5J5E3O7GGBBTDPFM/graph.json","fetch_events":"https://pith.science/api/pith-number/C4XH6SI5RH5J5E3O7GGBBTDPFM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C4XH6SI5RH5J5E3O7GGBBTDPFM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C4XH6SI5RH5J5E3O7GGBBTDPFM/action/storage_attestation","attest_author":"https://pith.science/pith/C4XH6SI5RH5J5E3O7GGBBTDPFM/action/author_attestation","sign_citation":"https://pith.science/pith/C4XH6SI5RH5J5E3O7GGBBTDPFM/action/citation_signature","submit_replication":"https://pith.science/pith/C4XH6SI5RH5J5E3O7GGBBTDPFM/action/replication_record"}},"created_at":"2026-05-18T01:25:46.111278+00:00","updated_at":"2026-05-18T01:25:46.111278+00:00"}