Problem:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.