Question

For whole numbers x and y, if xsquared + ysquared is a square, then prove why x and y cannot both be odd.

Answer 1

let x and y be odd numbers.
x=2m+1, y=2n+1

x^2=(2m+1)^2=4m^2+4m+1
y^2=(2n+1)^2=4n^2+4n+1

x^2+y^2 = 4m^2+4m+1+4n^2+4n+1 = 4m^2+4n^2 +4m+4n+2
we can see that there are terms that are not power of two.