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Math Help - stuck on a proof of x^n congr. 1 mod p

  1. #1
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    stuck on a proof of x^n congr. 1 mod p

    assumptions: p is a prime number.

    1<= a <= (p-1)

    the order of a modulo p is d

    d| (p-1)

    describe the solutions of the congruence x^d congr. 1 (mod p) in terms of a. Does this give all the solutions of x^d congr. 1 (mod p) ?


    I'm really blanking for some reason... obviously any power of a works but...where to go from there?
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  2. #2
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    Quote Originally Posted by minivan15 View Post
    assumptions: p is a prime number.

    1<= a <= (p-1)

    the order of a modulo p is d

    d| (p-1)

    describe the solutions of the congruence x^d congr. 1 (mod p) in terms of a. Does this give all the solutions of x^d congr. 1 (mod p) ?
    The solutions are 1,a,a^2,...,a^{d-1}.
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