Q12/125) Assume x and y are integers, such that (x^2+1)=2y. Now prove that y is the sum of squares of two integers?

x has to be odd so let x= 2m + 1

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

(x^2+1)/2 = y = 2m^2 + 2m + 1 = m^2 + (m+1)^2

proved