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Math Help - Primitive Root Theorem

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    Primitive Root Theorem

    Let m be an integer with m >2. If a primitive root modulo m exists, prove that the only incongruent solutions of the congruence x^2=1 mod m are x=1 mod m and x= -1 mod m.
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    Quote Originally Posted by mndi1105 View Post
    Let m be an integer with m >2. If a primitive root modulo m exists, prove that the only incongruent solutions of the congruence x^2=1 mod m are x=1 mod m and x= -1 mod m.
    If x^2\equiv 1(\bmod m) then write x\equiv r^y where r is a primitive root.
    Therefore, r^{2y}\equiv r^0 (\bmod m)\implies 2y\equiv 0(\bmod \phi(m) ).
    Thus, what can you conclude?
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