# Polynomial Rings

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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#### 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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