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# Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

12 weeks

#### Diagnostics

ARE YOU READY? DO YOU NEED THIS?

SYLLABUS
12 weeks

## Schedule

### AoPS Holidays

There are no classes October 31, November 25 ‐ December 1, December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, and August 29 ‐ September 1, 2025.

### Who Should Take?

This course is appropriate for students in grades 6-9 who have mastered basic algebra up through solving linear equations and manipulating multi-variable expressions. Students who have completed our Introduction to Algebra A course should have sufficient background. Students who are already proficient with modular arithmetic and basic Diophantine equations do not need this course. This course is roughly the same difficulty as our Introduction to Counting and Probability class. For those preparing for contests, this course should help with MATHCOUNTS and the AMC 8/10/12 tests.

### Lessons

 1 Integers, Fractions, Decimals, and Number Bases 2 Base Number Arithmetic 3 Multiples, Divisors, and Prime Numbers 4 Common Factors, Common Multiples, Euclidean Algorithm 5 Divisor Problems, More with the Euclidean Algorithm 6 Factorials, Special Integers, Algebra with Integers 7 Units Digit, Introduction to Modular Arithmetic 8 Calculations with Modular Arithmetic 9 Divisibility Rules and Multiplicative Inverses 10 Multiplicative Inverses, Solving Linear Congruences 11 Systems of Linear Congruences and the Chinese Remainder Theorem 12 Number Sense and Applications of Number Theory

### Required Textbook

 Introduction to Number Theory By Mathew Crawford A thorough introduction for students in grades 7-10 to topics in number theory such as primes & composites, multiples & divisors, prime factorization and its uses, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and more. Related course: Introduction to Number Theory

I liked this class because it taught me a lot of things that I didn't have the opportunity to learn in school. I learned a lot from it and I definitely think that this knowledge will help me in the future!