Thread: number thoery

Let m be within integers and with m>2, If a primitive root modulo m exists, prove that the only incongruent solutions of the congruence x^2 ≡1mod(m)are x ≡1mod(m) and x ≡-1mod(m)

Originally Posted by bigb

Let m be within integers and with m>2, If a primitive root modulo m exists, prove that the only incongruent solutions of the congruence x^2 ≡1mod(m)are x ≡1mod(m) and x ≡-1mod(m)

If is solution then where is primitive root. Then it means . Therefore, .
This congruence just has two solutions .
These two correspond to .