Sum of two squares

Number Theory Level 2

Is it true, that for any two coprime integers ( $x, y$ ), any of the positive divisors of $x^2+y^2$ can be expressed as sum of two perfect squares.

For example: If $x=1, y=3$ , then the statement above holds true (here $x^2+y^2=10$ ), because $\begin{aligned} 1 & = 0^2+1^2 \\ 2 & = 1^2+1^2 \\ 5 & = 1^2+2^2 \\ 10 & = 1^2+3^2 \end{aligned}$