Sum of two squares

Is it true, that for any two coprime integers (x,yx, y), any of the positive divisors of x2+y2x^2+y^2 can be expressed as sum of two perfect squares.

For example: If x=1,y=3x=1, y=3, then the statement above holds true (here x2+y2=10x^2+y^2=10), because 1=02+122=12+125=12+2210=12+32\begin{aligned} 1 & = 0^2+1^2 \\ 2 & = 1^2+1^2 \\ 5 & = 1^2+2^2 \\ 10 & = 1^2+3^2 \end{aligned}

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