Solving Congruence | Prime Numbers | 11^((p-1)/2) = 1 modp

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The discussion centers on solving the congruence equation 11^((p-1)/2) ≡ 1 (mod p) for prime numbers p. Participants reference Fermat's Little Theorem, which states that a^(p-1) ≡ 1 (mod p) for any prime p and integer a not divisible by p. The consensus indicates that the solution requires identifying primes p such that (p-1)/2 is also prime, leading to a specific subset of primes that satisfy the equation.

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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!
 
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regularngon said:

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: 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?
 
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...
 

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