Question

Show that every odd integer is of the form 4K+1 or 4K-1

Answer 1

Let a be any odd integer.

Then, a=2q+1 for some integer q, even or odd.

If q is even, then q=2k for some integer k and a=2(2k)+1=4k+1.

If q is odd, then q=2k-1 for some integer k and a=2(2k-1)+1=4k-1

Therefore every odd integer a is of the form 4k+1 or 4k-1.

Hope this will help you.