Polynomials which are locally reducible

2004/04/04 by Robert M. Guralnick, R. Guralnick, Murray Schacher +6
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT

paper · pdf · doi:10.48550/arxiv.math/0404069

arxiv created 2004/04/04 · openalex publication_date 2004/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a global field and n > 1 an integer. We show n is composite if and only if there is an irreducible polynomial f(x) ∈ K[x] of degree n which is reducible q-adically for all the primes q of K.

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