This has a solution only if "n" has the form "q"2 + "q" + 1. It is less simple to prove that a solution exists if "q" is a prime power. It is conjectured that these are the "only" solutions. It has been further shown that if a solution exists for "q" congruent to 1 or 2 mod 4, then "q" is a sum of two square numbers. This last result, the Bruck–Ryser theorem, is proved by a combination of constructive methods based on finite fields and an application of quadratic forms.