Question

Prove that the square of any positive integer is of the form 4q or 4q + 1 for some integer q.

Answer 1

To Prove: that the square of any positive integer is of the form 4q or 4q + 1 for some integer q.

Proof: Since positive integer n is of the form of 2q or 2q + 1

If n = 2q

If n = 2q + 1

Hence it is proved that the square of any positive integer is of the form 4q or 4q + 1, for some integer q.