Proving Congruences of Primes: Show 2^((p-1)/2) = +1 (mod p)

[johndoe3344]

I came across this:

Show that if p denotes an odd prime, then 2^((p-1)/2) = +1 (mod p).

So basically, this is asking me to show that p|2^((p-1)/2)-1 AND p|2^((p-1)/2)+1

But I'm stuck from there. What am I missing? Could someone help me with the proof?

 

[CRGreathouse]

Can you use Wilson's theorem?

So basically, this is asking me to show that p|2^((p-1)/2)-1 AND p|2^((p-1)/2)+1

No, replace the AND with OR.

 

[JSuarez]

The statement is called Euler's criterion for quadratic residues. The key to prove it is Fermat's theorem.