Purchase Solution

Polynomial Rings

Not what you're looking for?

Ask Custom Question

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.

Purchase this Solution

Solution Summary

This solution helps with a problem involving ring theory.

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 ...

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability