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Polynomial Rings

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Let p be any prime integer.
Consider polynomials f(x) and g(x) of the form:

f(x) = x^p
g(x) = x

over the finite field Zp.

Prove that f(c) = g(c) for all c in Zp.

Hint: Consider the multiplicative group of nonzero elements of Zp.

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https://brainmass.com/math/ring-theory/polynomial-rings-and-prime-integers-363491

Solution Preview

Since Zp is a field, all the non-zero elements of Zp form a group under "multiplication" (that is, multiplication modulo p).
There are p elements ...

Solution Summary

This solution helps with a problem involving ring theory.

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