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image of (x^2+y^2)/(u^2+v^2)

Source: VTRMC 2013 P4

May 13, 2021
number theoryalgebra

Problem Statement

A positive integer nn is called special if it can be represented in the form n=x2+y2u2+v2n=\frac{x^2+y^2}{u^2+v^2}, for some positive integers x,y,u,vx,y,u,v. Prove that
(a) 2525 is special; (b) 20142014 is not special; (c) 20152015 is not special.
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