# Prove this is divisible by 228 for any n

1. Oct 29, 2012

### sunnybrooke

1. The problem statement, all variables and given/known data
Prove that the following is divisible by 228 for any n (natural number).

$$1561^n + 712^n -1225^n - 364^n$$

2. Relevant equations
3. The attempt at a solution
I'm guessing you have to prove by induction. When n = 1, the quotient is 3. What do I do afterwards? Thanks.

2. Oct 29, 2012

### Simon Bridge

Welcome to PF;
You follow the other steps for induction.

3. Oct 30, 2012

### HallsofIvy

Staff Emeritus
In other words, assume that 1561k +712k −1225k −364= 228n for some integers k and n and then show that 1561k+1 +712k+1 −1225k+1 −364 is a multiple of 228.