# Advanced Problem Solving Module 9

### Advanced Problem Solving Module 9

Proof by induction is a really useful way of proving results about the natural numbers. If you haven't met this powerful technique before, this module will introduce you to the idea and method of induction. If you're already familiar, check out some of the problems and STEP questions that can be answered in this way!

This article gives an introduction to mathematical induction, a powerful method of mathematical proof.

Some statements which can be proved using induction, and some example proofs.

##### Age 16 to 18 Challenge Level:

Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) +
17^(2n+1) is divisible by 33 for every non negative integer n.

##### Age 16 to 18 Challenge Level:

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

Some STEP questions that can be solved using induction, and a worked example.