Sum of two squares

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 \[\begin{align} 1 & = 0^2+1^2 \\ 2 & = 1^2+1^2 \\ 5 & = 1^2+2^2 \\ 10 & = 1^2+3^2 \end{align}\]

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