Question

Prove that square of any integer leaves the remainder either 0 or 1 when divided by 4.​

Answer 1

2²=4

=>4/4=1 (leaving remainder 0)

3²=9

=>9/4=2¼ (leaving remainder 1)

4²=16

=> 16/4=4 (leaving remainder 0)

5²=25

=> 25/4=6¼(leaving remainder 1)

So, we conclude that square of any integer leaves the remainder either 0 or 1 when divided by 4.