Hello, Jacko!

If you don't have to use induction, an algebraic proof is faster.If is a positive odd integer, show that is divisible by 4

Let for some positive integer .

Then: .

Therefore: . is divisible by 4.

Use induction to prove: . for all positive integers

. . . yes!

Assume .for some integer

Add to both sides:

. .

Subtract 4 from both sides:

.

And we have: .

The left side is the left side of

The right side is divisible by 3.

The inductive proof is complete.