Explore BrainMass

Polynomial Rings

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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 March 21, 2019, 9:08 pm ad1c9bdddf

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.