Have a great winter break! Please note that AoPS Online will not have classes Dec 21, 2024 through Jan 3, 2025.

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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

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

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

Schedule

Friday
Sep 20 - Dec 13
7:30 - 9:00
PM ET
Sep 20 - Dec 13
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
$400 (~$34/lesson)
$400 (~$34/lesson)
CLOSED
Thursday
Feb 20 - May 8
7:30 - 9:00
PM ET
Feb 20 - May 8
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
$400 (~$34/lesson)
$400 (~$34/lesson)
ENROLL
Friday
Apr 11 - Jun 27
7:30 - 9:00
PM ET
Apr 11 - Jun 27
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
$400 (~$34/lesson)
$400 (~$34/lesson)
ENROLL

AoPS Holidays

There are no classes December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, August 29 ‐ September 1, October 31, and November 24 ‐ November 30, 2025.

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

After taking this class, I am solving AIME-IMO Number Theory Problems. This class really builds the foundations necessary for Olympiad Number Theory problems. It is also very problem-solving oriented which is great. I've learned so much from this class; Keep up the great work AoPS!