A further note on principal divisors in arithmetic progressions (Q2546914)

Assume that the class number \(h\) of an algebraic number field \(k\) is relatively prime to \((k : \mathbb Q)\) and that \(k/\mathbb Q\) is galois. If \((a,m)=1\), then there are infinitely many primes \(p\equiv a\bmod m\) which have principal prime ideal factors in \(k\).