**This course begins Summer 2021.**

For many math students learning a new topic can be uneasy and sometimes even cause apprehension. But often times, suddenly out of nowhere, is that feeling that you got it. You understand! Introducing Dave’s online math course Divisibility in the Integers. You’ll be glad it was him that taught it, because you’ll get that feeling over and over again.

## Who This Course is For

- Students in college who want to learn more mathematics.
- Anyone interested in divisibility in the integers.
- Students who are enrolled in Number Theory and want to improve their grade.
- Anyone interested in majoring in mathematics, physics, or engineering.
- Anyone wanting to learn about divisibility, primes, greatest common divisors, Euclidean algorithm, fundamental theorem of algebra, and linear Diophantine equations.

## Requirements

There is no required textbook, though you will need an up-to-date web browser, paper, and pen. A calculator is not necessary.

## What Youâ€™ll Learn in Divisibility in the Integers

- Definition of Divisibility
- Divisibility Lemmas
- The Division Algorithm
- Examples Using the Division Algorithm
- Sieve of Eratosthenes
- Prime Divisors
- Infinitude of Primes
- Definition of Greatest Common Divisors
- Bezoutâ€™s Identity
- Relatively Prime
- Euclidean Algorithm Lemma
- Euclidâ€™s Algorithm
- The Fundamental Theorem of Arithmetic
- Characterization of Primes
- Proof of the Fundamental Theorem
- Least Common Multiples
- What are Diophantine Equations?
- Two Variable Linear Diophantine Equations
- Solving Linear Diophantine Equations
- Multivariable Linear Diophantine Equations

## Course Description

This course is a continuation of the course entitled The Natural Numbers. You are required to know mathematical induction for this course.

This course begins with the definition of divisibility in the integers and then discusses the division algorithm in great detail. We then discuss the prime numbers (the fundamental building blocks of the integers).

Then we examine the greatest common divisors of two integers and how to find them using the Euclidean algorithm. After this, we state and prove the fundamental theorem of arithmetic. Towards the end of the course, we include linear Diophantine equations. We emphasize solvability and solve many examples.

## Recommended Prerequisites for Divisibility in the Integers

I recommend the prerequisite course The Natural Numbers. If you’re not sure if this course is for you, checkout the course contents below or find out more by checking out my free number theory articles.