a = 1 n cannot be odd from this summing, so n must have at least a factor of 2 ===> b = 2 Because n is even then c and d must be a pair of even-odd numbers With the sum of two even and two odd squares, n = 2 mod 4, so it must be that c is odd and d = 2c n = 1^2 + 2^2 + c^2 + (2c)^2 = 5 × (1 + c^2) Since 5 | n, then c = 5 only Answer, n = 5 × (1^2 + 5^2) = 130