Decomposing integers - Colegiul Național din Iași (Iași - Roumanie)

What are the integers that can be written as x^2 + ay^2, where a is a fixed integer? Important cases: a=1, -1, 2, -2. Example: take a = 1; the number 5 can be written as 1^2 + 2^2, but 7 cannot be written as x^2 + y^2.