Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 142-01. Deterministic Polynomial Factorization over Prime Fields
Manuscript map · lines 5165–5174
OpenAI@2026-10-07#rem:oai-p-142-01
Authors: OpenAI. Family 142.
Title: Deterministic Polynomial Factorization over Prime Fields.
Abstract: We give a uniform deterministic polynomial-time algorithm for complete factorization over prime fields. For a prime p in binary and a nonzero polynomial $f{}in{}mathbf F_p[x]$ given by its dense coefficient list, the algorithm computes the irreducible factors and their multiplicities using a number of bit operations polynomial in $({}deg f+1){}log p$. The proof uses the uniform Hecke zero-free theorem from the companion paper *Primitive roots for every admissible integer base*.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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