YongTao Chen has a MSc in pure mathematics, and has been an university math teacher for over two decades. His teaching focuses on Advanced Calculus, Linear Algebra, Abstract Algebra, Real Analysis, and Elementary Number Theory. He also taught Mathematical Logic, Introductory Probability, and Category Theory. Since the year 2011, he has been teaching online mathematical courses with enthusiasm.

Elementary Number Theory is such a charming subject of mathematics that many great mathematicians devoted to it because of its wealth of easily accessible and fascinating questions, and its intellectual appeal. Gauss once remarked that "mathematics is the queen of the sciences and arithmetic the queen of mathematics". This 3-week long course imparts the primary coverage of the subject, which pave the way to further study of more advanced courses.

Elementary Number Theory is the study of the basic structure and properties of integers. Learning Number Theory helps improving one's ability of mathematical thinking. Successful completion of this course will enable you to:

- Prove results involving divisibility and greatest common divisors;
- Solve systems of linear congruences;
- Find integral solutions to specified linear Diophantine Equations;
- Apply Euler-Fermat’s Theorem to prove relations involving prime numbers;
- Apply the Wilson’s theorem.

Taking this course assumes no specific background knowledge other than the patience to work about 6 hours each week. Anyone who wants a taste of the glamour of mathematics is welcomed to enrol in this course. I trust that this course will be of some benefit to all who engage with it, and hope that taking part in this compact course could be felt like making a fun excursion.

The course consists of 6 lectures, each of which contains two periods of lessons. In the spirit of teachings in reality, in each week are delivered two lectures, and the lecturing on the entire course is thus completed in 3 weeks.

The experience indicates that the attainment of an ideal teaching and learning effect mainly depends on how the lecture notes are written. The efforts into writing present lecture notes in this course were focused on three aspects: self-containnedness, conciseness, as well as logic coherence. The examples given in the course are carefully selected. The lecture notes is the fruit of many years' experience in teaching. So you are expected to read the notes seriously first. Then you are encouraged to try doing the relevant exercises, most of which are more or less directly related to corresponding definition, example, or proposition. The homework assignment for each lecture consists of more challenging problems.

A discussion forum for each week is set up so as to provide opportunities for you to interact with other people. You are encouraged to ask your own questions about the contents in corresponding lectures of the week. You can also learn by answering questions from other people.

In order to test your understanding of what you have learned from the entire course, a set of review problems at medium level of difficulty is proposed at the end of the course.

This self-contained course on Elementary Number Theory imparts the primary coverage of the subject. Topics include: Divisibility, Division algorithm, Primes and Composites, Greatest Common Divisors, Least Common Multiples, Fundamental Theorem of Arithmetic, Linear Diophantine Equations, Congruences, the Chinese Remainder Theorem, Euler-Fermat's Theorem, and Wilson's Theorem.

YongTao Chen has a MSc in pure mathematics, and has been an university math teacher for over two decades. His teaching focuses on Advanced Calculus, Linear Algebra, Abstract Algebra, Real Analysis, and Elementary Number Theory. He also taught Mathematical Logic, Introductory Probability, and Category Theory. Since the year 2011, he has been enthusiastically teaching online mathematical courses.

#### 1st Week-Lecture 1: Divisibility of Integers

#### 1st Week-Lecture 2: Greatest Common Divisors

#### 2nd Week-Lecture 3: Fundamental Theorem of Arithmetic

#### 2nd Week-Lecture 4: Congruence

#### 3rd Week-Lecture 5: Chinese Remainder Theorem

#### 3rd Week-Lecture 6: Euler’s and Wilson’s Theorems

#### Review Problems