Question

Show that the square of an odd positive integer is of the form 8q + 1, for some integer q.

Answer 1

To Prove: that the square of an odd positive integer is of the form 8q + 1, for some integer q.

Proof: Since any positive integer n is of the form 4m + 1 and 4m + 3

If n = 4m + 1

If n = 4m + 3

Hence n² integer is of the form 8q + 1, for some integer q.