Question

prove that the square of any intger leaves the remainder either zero or one when divided by 4

Answer 1

Case 1: n = 2 x n=2x

Then n 2 ≡ 4 x 2 ≡ 0

mod  4 n2≡4x2≡0 mod 4

Case 2: n = 2 x + 1 n=2x+1

Then n 2 ≡ 4 x 2 + 4 x + 1 ≡ 4 ( x 2 + x ) + 1 ≡ 1  

mod  4

If you try it also works