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Math Help - Primitive Root Problem

  1. #1
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    Primitive Root Problem

    Let p be an odd prime. Prove that r is a primitive root modulo p if, and only if, r \in Z^+ such that gcd (r,p) = 1 and
    r^{(p-1)/q} is not congruent to 1 mod p

    for all prime divisors q of p-1
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  2. #2
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    Quote Originally Posted by Janu42 View Post
    Let p be an odd prime. Prove that r is a primitive root modulo p if, and only if, r \in Z^+ such that gcd (r,p) = 1 and
    r^{(p-1)/q} is not congruent to 1 mod p

    for all prime divisors q of p-1

    Direction ==> is immediate from definition, and direction <== follows from assuming that ord(r) = m < p-1

    and then dividing p-1 by m.

    Tonio
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