Question: How many distinct congruence classes are there modulo x^2+x+1 in Z5[x]? Can you find polynomials u(x) and v(x) in Z5[x] for which 1=u(x)*(x+2)+v(x)*(x^2+x+1)? (Hint: long

How many distinct congruence classes are there modulo x^2+x+1 in Z5[x]? Can you find polynomials u(x) and v(x) in Z5[x] for which 1=u(x)*(x+2)+v(x)*(x^2+x+1)?

(Hint: long division gives (x^2+x+1)=(x+2)*(x-1)+3, and 3 is invertible in Z5)

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