On the Distribution of Integer Solutions of f(x, y) = z2 for a Definite Binary Quadratic Form f

Abstract

Let f be a positive definite binary quadratic form with rational coefficients. We shall call a point (x, y) in E2 with integers x and y a Pythagorean point of f when f(x, y) = z2 is satisfied with some integer z, and shall prove the following theorem.