Prove that there is a positive integer that can be written as the sum of squares of positive integers in two different ways. (Use a computer or calculator to speed up your work.)

Solution Step 1 In this problem, we have to prove that there is a positive number which can be written as the sum of a square of the positive number. Step 2 Let us assume that n be the positive number. n = = where x, y, p and q be a positive number. According to the complex number, product of complex number and their conjugate is always be real positive number. Let us assume that z = x + iy and conjugate (z) = x - iy Multiply both of the equation we get, Real positive number = (x + iy)(x - iy) = Here, real positive number is n