Question

Prove that the square of any positive integer of the form 5q + 1 is of the same form.

Answer 1

Let n = 5q + 1 where q is a positive integer

∴ n² = (5q + 1)²

= 25q² + 10q + 1

= 5(5q² + 2q) + 1

= 5m + 1, where m is some integer

Hence, the square of any positive integer of the form 5q + 1 is of the same form.