Question 191
Distinct positive integers $A$ and $B$ are given. Prove that there exist infinitely many positive integers that can be represented both as $x_1^2 + Ay_1^2$ for some positive coprime integers $x_1$ and $y_1$, and as $x_2^2 + By_2^2$ for some positive coprime integers $x_2$ and $y_2$. (Golovanov A.S.)