Intermediate Number Theory
Number theory using algebraic techniques, multiplicative functions, Diophantine equations, modular arithmetic, Fermat's/Euler's Theorem, primitive roots, and quadratic residues. Much of the first half of the class emphasizes using the basic tools of the Introduction class in clever ways to solve difficult problems. In the second half, more theory will be developed, leading students to the beginning Olympiad level.

12 weeks

12 weeks
ARE YOU READY?
DO YOU NEED THIS?


Schedule
Spring 2020  This course will be offered in Spring 2020. Click here to join our mailing list to be notified when the course schedule is available. 
AoPS Holidays
There are no classes November 25–December 1, or December 21–January 3.
Who Should Take?
Students should have a complete understanding of modular arithmetic, and a mastery of algebra through our
Intermediate Algebra class (or a typical honors Algebra 2 class and some Precalculus) before taking this class.
Lessons
Lesson 1 
Introduction 
Lesson 2 
Bases 
Lesson 3 
Divisibility 
Lesson 4 
Divisors and Multiplicative Functions 
Lesson 5 
Prime Factorizations 
Lesson 6 
Algebra in Modular Arithmetic 
Lesson 7 
Linear Diophantine Equations 
Lesson 8 
Perfect Squares 
Lesson 9 
Fermat's Little Theorem and Euler's Theorem 
Lesson 10 
Orders and Primitive Roots 
Lesson 11 
Quadratic Residues and Squares 
Lesson 12 
Sums of Two Squares 