(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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- Nov 9th 2008, 09:48 AMmndi1105primitive 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? - Nov 9th 2008, 09:55 AMThePerfectHacker
You have, $\displaystyle x(x-1)\equiv 0(\bmod 6)$. Thus, $\displaystyle x=0,1,3,4$. Therefore, there are six solutions up to congruence.

Quote:

(b) why does the behavior exhibited in part (a) not violate Lagrange's Theorem?

- Nov 11th 2008, 02:27 PMmndi1105
How did you get that there were 6 incongruent roots modulo 6?

- Nov 11th 2008, 02:31 PMwhipflip15
I think that was a mistake.

- Nov 11th 2008, 07:34 PMThePerfectHacker