Solution
= Solution
<Dirichlet theorem on primes in arithmetic progressions> states that if <positive integer> $q$ and <integer> $a$ satisfy $\gcd(a,q)=1$, then infinitely many <prime numbers> satisfy
$$
\boxed{p\equiv a\pmod q.}
$$
The coprimality hypothesis is essential: if $a$ and $q$ have a common factor greater than one, a <prime> in the progression must divide that factor, giving at most finitely many possibilities.