This exercise wants me to prove that for each $m \in \mathbb{Z}$ there are infinitely many primes $p \equiv 1 \pmod{m}$. It seems that this can be based on the fact that $f$ has a root mod $p$ for infinitely many primes $p$ whenever $f$ is a nonconstant polynomial over $\mathbb{Z}$. This is from the exercise 30 on chapter 3 of Marcus' Number Fields. Please help me.
2026-04-28 08:27:14.1777364834
Marcus number fields exercise 30 chapter 3
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