Prove this is divisible by 228 for any n

[sunnybrooke]

Homework Statement

Prove that the following is divisible by 228 for any n (natural number).

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

Homework Equations

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.

 

[Simon Bridge]

Welcome to PF;

I'm guessing you have to prove by induction. When n = 1, the quotient is 3. What do I do afterwards? Thanks.

You follow the other steps for induction.

 

[HallsofIvy]

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