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A related problem is to construct an irreducible polynomial of degree $r^e$ (where $r$ is a prime) over a given finite field $\\mathbb{F}_q$ of characteristic $p$ (equivalently, constructing the bigger field $\\mathbb{F}_{q^{r^e}}$). Both these problems have famous randomized algorithms but the derandomization is an open question. We give some new connections between these two problems and their variants.\n  In 1897, Stickelberger proved that if a polynomial has an odd number of even degree factors, then it"},"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":"1702.00558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-02-02T07:20:18Z","cross_cats_sorted":["math.AC","math.NT"],"title_canon_sha256":"fc8220d89271688ea4e38228db1e5775c20cc77705ebfc3a988dd4dcac097f74","abstract_canon_sha256":"0130e6969669192d0698a4142036807828e9d3cfda26d644d8b9dbf845758a84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:33.253228Z","signature_b64":"4VrewZ/fdpuXNzNJJVRgxkQ0Au4R5aeoOx2MhJTfGLqf1o+IoPeqeyYm4e6nRspXjLUzUY12wSQ1AxVDct+wCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3be24d87a96af2e5650b49b8d63a39fb1121870905c76123b6997743bfe978e2","last_reissued_at":"2026-05-18T00:51:33.252816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:33.252816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Irreducibility and r-th root finding over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"cs.CC","authors_text":"G\\'abor Ivanyos, Nitin Saxena, Rajat Mittal, Vishwas Bhargava","submitted_at":"2017-02-02T07:20:18Z","abstract_excerpt":"Constructing $r$-th nonresidue over a finite field is a fundamental computational problem. 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