# Homework Help: Prove a^5 congruent to a (mod 15)

1. Feb 3, 2010

### sty2004

1. The problem statement, all variables and given/known data
Prove that a5 $$\equiv$$a (mod 15) for every integer a.

2. Relevant equations

3. The attempt at a solution
I do not know how to show a5-a is divisible by 15

2. Feb 4, 2010

### Mandark

$$a^5 - a = (a-1)a(a+1)(a^2 + 1)$$ can you show that this expression is divisible by 3 and by 5 individually? This would imply it's divisible by 15.