Question

Prove that the square of any integers leaves the remainder either 0 or 1when divided by 4?

Answer 1

Every integer when squared leaves a the remainder 0 or 1 when divided by 4. So, every even integer squared leaves a remainder 0 when divided by 4. And every odd integer squared leaves a remainder 1 when divided by 4. Hence, any integer squared leaves a reminder 0 or 1 when divided by 4.