In number theory, the Ankeny–Artin–Chowla congruence is a result published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla. It concerns the class number h of a real quadratic field of discriminant d > 0. If the fundamental unit of the field is with integers t and u, it expresses in another form for any prime number p > 2 that divides d. In case p > 3 it states that where and \chi; is the Dirichlet character for the quadratic field. For p = 3 there is a factor (1 + m) multiplying the LHS. Here represents the floor function of x. A related result is that if d=p is congruent to one mod four, then where Bn is the nth Bernoulli number. There are some generalisations of these basic results, in the papers of the authors.