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Scholars Math 9.2: Intermediate Number TheoryNumber 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? SYLLABUS |
Schedule
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Sunday
Jun 7 - Aug 30 |
7:30 - 9:00 PM ET
Jun 7 - Aug 30
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 |
Marco Figueroa Ibarra | $415 (~$35/lesson) |
$415
(~$35/lesson)
Few Spots Left! |
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STARTING SOON |
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Friday
Jun 19 - Sep 11 |
7:30 - 9:00 PM ET
Jun 19 - Sep 11
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 |
Martha Maria Bernal Guillen | $415 (~$35/lesson) |
$415
(~$35/lesson)
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Sunday
Sep 27 - Dec 20 |
7:30 - 9:00 PM ET
Sep 27 - Dec 20
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 |
Jeffery Yu | $415 (~$35/lesson) |
$415
(~$35/lesson)
|
| Spring 2027 | This course will be offered in Spring 2027. Click here to join our mailing list to be notified when the course schedule is available. | |||
AoPS Holidays
There are no classes July 3 ‐ 5, September 5 ‐ 7, November 23 ‐ 29, December 21 ‐ January 3, February 13 - 15, and May 29 ‐ May 31 2027.
Who Should Take?
Students should have a complete understanding of modular arithmetic, and a mastery of algebra through our Scholars Math 9: 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 |
