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33 LIVE: Number Theory

Ma/Mi/J/V/L 9:00–10:30pm desde {{firstDateM}/{{firstDateD}} (hora del Este de EE. UU.)

Inscribirse $599Todos los detalles del curso

El curso de LIVE tiene un total de 30 horas de formación de video en vivo (~20/hora), más 1 año de acceso a los videos pregrabados del curso del Prof. Loh.

We’ve carefully designed our courses to maximize engagement. Each of our LIVE classrooms has at least one staff member for every 13 students. The typical class size is around 30 students.

* The official meeting time for this course is 5:00pm in New York.

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Analiza el examen asignado como tarea

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Comentarios

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

AH

Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.

JS

Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!

AZ

Worth everything and learned a lot

DX

Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.

YP

Great job

SK

I absolutly loved this course

LZ

This course is incredible! It taught me many, many tricks that I never knew! Very helpful!

JN

Absolutely worth everything!!

AB

Excellent course

GK

Great explanation

Plan de estudios

Los 20 encuentros del curso se dividen en 16 lecciones (llamadas Día 1 hasta Día 16) y 4 horas para analizar los exámenes de tarea. Cada encuentro para analizar un examen es luego de 4 lecciones.

Día 1

Remainder mod 10; definition of modular congruency; notation of a modulo b; remainders of n²; modular addition, subtraction and multiplication; remainders modulo 11; negative remainders

Día 2

Explanation and motivation for divisibility rules for 3 and 9 and shortcuts for their use; sum and average of an arithmetic progression; triangular numbers; modular multiplication

Día 3

Explanation and motivation for divisibility rules for 2, 4, and 8 and shortcuts for their use; permutations; divisibility by 12; sum and average of arithmetic progression; negative remainders

Día 4

Remainders after dividing by 99; factors; patterns in multiples of 9 mod 1; palindromic numbers; factors of 1001 and 1111; negative remainders; remainders mod 11; arithmetic progression

Día 5

Prime factorization; number of factors; sum of factors; average of factors; sum of reciprocals of factors; product of factors; factors of 111; expanding factors; sum of consecutive powers of 2; geometric series

Día 6

Number of zeroes at the end of combinatorial expressions such as factorial; modular multiplication; floor function; ways to choose n objects; sum of consecutive powers of 2;

Día 7

Least Common Multiple (LCM); Greatest Common Divisor (GCD); prime factorization; product of LCM and GCD; quotient of LCM and GCD; factorials

Día 8

Motivation for and examples of Euclidean Algorithm for finding GCD; Fibonacci numbers; factors of 111; relatively prime numbers

Día 9

Relatively prime numbers; pattern of cycling remainders; remainders of multiples of 2, 3, 4, 5, 6, 7, 8 and 9; Venn diagram; Inclusion / exclusion; Euler's Totient Function

Día 10

Chinese Remainder Theorem and use with composite moduli; negative remainders; solving sets of congruences; LCM; remainders of multiples of 6 mod 5; negative remainders

Día 11

Chinese Remainder Theorem with non-relatively-prime moduli; remainders of multiples of 9 mod 12; cycles of remainders of multiples of 9; LCM; reduction of systems of congruences; unsolvable congruences

Día 12

Systems of three congruences; Euler's Totient Function; remainders modulo composite numbers; pairwise relatively prime numbers; Venn diagram; factoring; combinatorial counting

Día 13

Factoring tricks for solving algebraic equations; area and perimeter of rectangles; number of ways to factor; equations in 1/x; impossibility of division by 0; number of integers solutions to an equation

Día 14

Remainders of powers; cycles of remainders of powers; pattern of last two digits of powers of 7; remainders of powers of 7 mod 4; power towers

Día 15

Multiplicative inverses with respect to a modulus; explanation and motivation for divisibility trick for 7; repeating cycles of remainders

Día 16

Terminating decimals and their fraction representations; repeating periods of repeating decimals; proof of why square root of 2 is irrational; prime factorization; proof techiques and directions of logic; proof by contradiction

Co-Estrellas

Foto de perfil de Eric Zhan
ERIC ZHAN

National MATHCOUNTS competitor for Washington • 2022 USAJMO winner • Likes to swim

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Foto de perfil de Lillian Xia
LILLIAN XIA

MPFG Invite • AIME Qualifier • Enjoys playing tennis

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Poliza De Reembolso

Las solicitudes de reembolso no se aceptaran despues de la segunda sesion del estudiante de LIVE; Cantidad revuelta: 90% reembolso en el metodo original de pago o 100% reembolso en creditos para cursos.