There exists a prime congruent to $m$ mod $p$
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Q: Is every element of $mathbb Z/pmathbb Z$ represented by a prime number? More generally, let $m, n in mathbb Z$ be coprime. Is there a prime number congruent to $m$ modulo $n$? the affirmative answer is given by Dirichlet's theorem. A: Yes, in fact there are infinitely many such primes. I don't want to prove Dirichlet's theorem. Is it obvious that there always exists at least one such prime?
elementary-number-theory
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asked Dec 2 '15 at 5:31
Ben
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