Question

If x and y are odd positive integers then x^2 y^2 is not divisible by 4

Answer 1

Answer:

Let the two odd positive numbers be x = 2k + 1 and y = 2p + 1

Hence x² + y² = (2k + 1)² + (2p + 1)²

                    = 4k² + 4k + 1 + 4p² + 4p + 1

                    = 4k² + 4p² + 4k + 4p + 2

                    = 4(k² + p² + k + p) + 2

Clearly notice that the sum of square is even the number is not divisible by 4

Hence if x and y are odd positive integers, then x² + y² is even but not divisible by 4