Finding primes p where 11^((p-1)/2) ≡ 1 (mod p)

[regularngon]

Homework Statement

Find all primes p (as a congruence) such that 11^((p-1)/2) = 1 modp

The Attempt at a Solution

I'm new to congruences and I don't really know to approach this. Any help greatly appreciated!

 

[HallsofIvy]

Homework Statement

Find all primes p (as a congruence) such that 11^((p-1)/2) = 1 modp

The Attempt at a Solution

I'm new to congruences and I don't really know to approach this. Any help greatly appreciated!

That looks like a candidate for Fermat's Little Theorem: a^p-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?

 

[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...