Exam 4: Basic Concepts in Number Theory and Finite Fields

A ring is said to be _________ if it satisfies the condition ab = ba for all a,b in R.

Finite fields play a crucial role in several areas of cryptography.

If we attempt to perform polynomial division over a coefficient set that is not a field,we find that division is not always defined.

The rules for ordinary arithmetic involving addition,subtraction,and multiplication carry over into modular arithmetic.

A zero-degree polynomial is called a __________ polynomial and is simply an element of the set of coefficients.

If a is an integer and n is a nonzero integer,we define a mod n to be the remainder when a is divided by n.The integer n is called the __________ and the remainder is called the residue.