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life is maths
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Homework Statement
Hi, my question is:
Show that if p is a prime, x2≡1(mod p) has exactly two solutions for p>2.
Homework Equations
The Attempt at a Solution
I did:
p|x2-1
Then for a number a;
pa=x2-1
pa+1=x2
x=[tex]\mp[/tex][tex]\sqrt{pa+1}[/tex]
But I did not use the fact that p is prime and greater than 2. Do you have any ideas? Thanks in advance.
This is not a homework but a suggested exercise before exam.