If Two Numbers are Expressible as Sums of Two Squares and One Divides the Other, Is the Result Also Expressible As a Sum of Two Squares?

\[n, \; m\]
  can each be written as the sum of two squares and  
, can we write  
  as the sum of two squares?
Yes it is. Each prime  
  of the form  
  which divides  
\[n, \;m\]
  must occur as even powers, with the power in the decomposition of  
  greater than in the decomposition of  
The result follows using When an Integer Can be Expressed as a Sum of Two Squares.
For example,  
  and is divisible by  

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