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## Number Theory

#### Learning Objectives

On completing this chapter, you should be able to:

• state the definitions of a factor and a multiple of an integer

• state and prove the division algorithm

• define the ideas of the greatest common divisor (gcd) and the least common multiple (lcm)

• define a pair of relatively prime numbers

• use the Euclidean algorithm to find the gcd

• find the gcd and lcm of pairs of numbers by prime factorization

• define a prime number

• define congruence classes and congruence relations

• solve linear congruence equations for small numbers

• state and prove Fermat's theorem and its generalization due to Euler

##### 7.1 INTRODUCTION AND MOTIVATION

There was a time when Number Theory was considered a very pure subject in the sense ...

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