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Math Help - Suppose that a has order 3 modulo...

  1. #1
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    Suppose that a has order 3 modulo...

    Suppose that a has order 3 modulo some p. Prove that a+1 has order 6 modulo p. [Hint: Take a^3 - 1 (which is 0 modulo p) and factor it to get a new expression for a+1.]
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    MHF Contributor Bruno J.'s Avatar
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    Well clearly a \neq 1. Since 0=a^3-1=(a-1)(a^2+a+1) we have 0=a^2+a+1. I think you can take it from here!
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    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by NikoBellic View Post
    Suppose that a has order 3 modulo some p. Prove that a+1 has order 6 modulo p. [Hint: Take a^3 - 1 (which is 0 modulo p) and factor it to get a new expression for a+1.]
    See here.
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