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Arithmetic Sequences and Euler's Theorem

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I really need some help with this. Someone has got to have the background for this one.

"Let p1(x) = x^3 + x + 1 and p2(x) = x^3 + s + 2 in F5[x]. F5[x] is ust the set of all polynomials in x with coefficients from the set {0,1,2,3,4} with arithmetic done mod 5. Compute (x+2)^2114 in F5[x]/(p1(x)) and in F5[x]/(p2(x)). The hint is: one of p1(x) and p2(x) is irreducible, the other isn't.

However, we are told to use the result of another problem that states: State and prove a variant of Euler's theorem (If n>1 is an integer and gcd (a,n) = 1 then a^phi(n) =1(mod n) ) for polynomials in F[x]/(m(x)), where m is in F[x] and F is a finite field.

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This solution helps with arithmetic sequences and Euler's theorem.

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