Solving a congruence

1. Feb 12, 2008

regularngon

1. The problem statement, all variables and given/known data
Find all primes p (as a congruence) such that 11^((p-1)/2) = 1 modp

3. The attempt at a solution
I'm new to congruences and I don't really know to approach this. Any help greatly appreciated!

2. Feb 12, 2008

HallsofIvy

Staff Emeritus
That looks like a candidate for Fermat's Little Theorem: ap-1 is congruent to 1 for any prime p and any a not a multple of p. For what prime p is (p-1)/2 also a prime?

3. Feb 12, 2008

regularngon

Thanks for the reply. I did a few computations and indeed it seems to only hold for when (p-1)/2 is also a prime. I still don't see how Little Fermat implies this though...