# If p is prime

1. Oct 24, 2013

### Amannequin

1. The problem statement, all variables and given/known data

If p is a prime and p>3, show that pr$\equiv$1,5,7 or 11 (mod12)

2. Relevant equations

3. The attempt at a solution

2. Oct 24, 2013

### Dick

Show any other possibility doesn't work. For example, suppose $p^r\equiv 2 (mod 12)$. What's wrong with that?

3. Oct 24, 2013

### brmath

If k is an odd number, list the possibilities for k mod 12.
Next if p is a prime > 3, list the possibilities for p mod 12.
Then what conclusion can you draw about $p^r$?