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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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    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.