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.© BrainMass Inc. brainmass.com April 3, 2020, 9:09 pm ad1c9bdddf
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 ...
This solution helps with a problem involving ring theory.