Intermediate Number Theory

Name: Intermediate Number Theory
Price: 400 USD

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

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

SYLLABUS

12 weeks ARE YOU READY? DO YOU NEED THIS? SYLLABUS

Schedule

Sunday Jun 1 - Aug 24	7:30 - 9:00 PM ET Jun 1 - Aug 24 7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones	Eli Brottman	$400 (~$34/lesson)	$400 (~$34/lesson) CLOSED
Wednesday Jun 18 - Sep 3	7:30 - 9:00 PM ET Jun 18 - Sep 3 7:30 - 9:00 PM Eastern 6:30 - 8:00 PM Central 5:30 - 7:00 PM Mountain 4:30 - 6:00 PM Pacific Click here to see more time zones	Dan Kinch	$400 (~$34/lesson)	$400 (~$34/lesson) CLOSED
Fall 2025	This course will be offered in Fall 2025. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes August 29 ‐ September 1, October 31, November 24 ‐ November 30, December 20 ‐ January 2, May 23 ‐ 25, and July 3 ‐ 5, 2026.

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

1	Introduction
2	Bases
3	Divisibility
4	Divisors and Multiplicative Functions
5	Prime Factorizations
6	Algebra in Modular Arithmetic
7	Linear Diophantine Equations
8	Perfect Squares
9	Fermat's Little Theorem and Euler's Theorem
10	Orders and Primitive Roots
11	Quadratic Residues and Squares
12	Sums of Two Squares