Question 2
A2 (SWE). Let $a$ and $b$ be nonnegative integers such that $ab\ge c^2$, where $c$ is an integer. Prove that there is a number $n$ and integers $x_1,x_2,\ldots,x_n,y_1,y_2,\ldots,y_n$ such that
$$\sum_{i=1}^n x_i^2=a,\qquad\sum_{i=1}^n y_i^2=b,\qquad\sum_{i=1}^n x_iy_i=c.$$
$$\sum_{i=1}^n x_i^2=a,\qquad\sum_{i=1}^n y_i^2=b,\qquad\sum_{i=1}^n x_iy_i=c.$$