Hi everyone,

First time poster. This is probably an embarrassingly easy problem. I'm a non-maths student working through an intro to proof book in my spare time and there are problem sets with no solutions. I've got stuck on a couple of problems. This is one of them.

**Question**: Prove by induction on

that, for all positive integers

,

divides

.

I know where I need to go with this, I think, I'm just stuck on the inductive step:

**Proof**: We use induction on n. If

divides

, then

for some integer

.

Base case: If

, then

, where

, proving the base case.

Inductive step: Suppose as inductive hypothesis that

for some integer

. Then

(by inductive hypothesis).

That's as far as I get. Obviously, by definition, but I get stuck there.

Thanx in advanx!

EDIT: not sure how to add the solved prefix, hope this is an okay ad hoc measure.