Wednesday, 5 August 2015

number theory - Congruence in mathbbZ5[x]

I'm not really sure how to approach this problem, since it doesn't seem similar to solving linear congruences in Zm.



Find all solutions in Z5[x] to the congruence (x^2-1)a(x)\equiv x^2+x-2\pmod{x^3-1}. Additionally, is it possible to count the number of solutions in (\mathbb{Z}_5[x])_{x^3-1} without actually finding them?



Any help is appreciated.

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