Ankeny–Artin–Chowla congruence

The Ankeny–Artin–Chowla congruence is a result in number theory concerning prime numbers and their distributions. Specifically, it deals with the congruence relationship of prime numbers in the context of quadratic residues. The conjecture can be stated as follows: For any odd prime \( p \) and any integer \( a \) that is relatively prime to \( p \), there exists a prime \( q \equiv a \pmod{p} \).