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Math Help - primitive roots for primes

  1. #1
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    primitive roots for primes

    (a) find the number of incongruent roots modulo 6 of the polynomial f(x)=x^2 - x
    (b) why does the behavior exhibited in part (a) not violate Lagrange's Theorem?
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    Quote Originally Posted by mndi1105 View Post
    (a) find the number of incongruent roots modulo 6 of the polynomial f(x)=x^2 - x
    You have, x(x-1)\equiv 0(\bmod 6). Thus, x=0,1,3,4. Therefore, there are six solutions up to congruence.
    (b) why does the behavior exhibited in part (a) not violate Lagrange's Theorem?
    Because that theorem applies only for f(x) \equiv 0 (\bmod p) where p is a prime.
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    How did you get that there were 6 incongruent roots modulo 6?
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    I think that was a mistake.
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    Quote Originally Posted by mndi1105 View Post
    How did you get that there were 6 incongruent roots modulo 6?
    Quote Originally Posted by whipflip15 View Post
    I think that was a mistake.
    Of that is is a mistake! If you look above we get four solutions if you count them, but I wrote six.
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