Kunze Linear Algebra · Problem 4.5.8

Polynomials

Mathematics — Methods · congruence-irreducible-zero-divisors

Problem

If pp is an irreducible polynomial and fg≡0 mod pfg \equiv 0 \bmod p, prove that either f≡0 mod pf \equiv 0 \bmod p or g≡0 mod pg \equiv 0 \bmod p. Give an example which shows that this is false if pp is not irreducible.

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