数论工具图标

LIVE 90: 数论工具

9月2日起,每周六上午12:00–1:30 (您所在地当地时间)

报名课程 $599课程详细介绍

该模块直播课总计30小时,课时费约为(~$20/小时)。报名直播课将同时享受该模块对应录播课程(Pre-Recorded Course)一年有效,无限次回看。

课程师生比不低于1:13。老师们将用各种方式鼓励孩子们发言、提问和思考,最大限度地提高孩子们的课堂参与度和积极性。每个班次不超过40名学生。

* 该班次直播课上课标准时间为下午8:00,纽约时间。

由于您所在国家的夏令时调整与本课程大部分学生所在地的时区不同,因此您的上课时间将在本课程期间发生变化,请注意调整您的课程安排。

不知道课程是否合适?来挑战一下能力水平测试吧!

这门课会难度太大吗?(基础能力测试)这门课会太简单吗?(分级测试)

课程日历

上课日由彩色图例标识。点击任意上课日了解当天课程内容

图例

16节日挑战课程(Day X Challenge),通过不同的数学问题学习新的知识内容

4节单元复习课程(Week X Challenge),集中解决单元测验中遇到的问题

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学生评价

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

课程大纲

LIVE在线直播课程每个模块包含【16次日挑战课程(第1课到第16课)+ 4次单元复习课(回顾单元测验Week Challenge 1到4)】共20节直播课程。学生将同时享受该模块对应录播课程(Pre-Recorded Course)一年有效。每四节日挑战直播课结束后将有一次单元考核测验,巩固前4节课学习到的知识内容,帮助学生进一步内化思考。学生需要在复习课前进入Pre-Recorded课程完成单元测验。

第1课

模10的余数、模算数、模算数的表示方法、n2 的余数、模加法、减法和乘法、模11的余数、负余数

第2课

整除 3 和 9 的规则、技巧及其应用详解、等差数列求和与平均值、三⻆数、模乘法

第3课

详解整除2、4、8的规则、技巧及其应用详解、排列、整除12的规则、等差数列求和与平均值、负余数

第4课

模99的余数、因数、除以9余1的数的规律、回文数字、1001 和1111的因数、负余数、模11的余数、等差数列

第5课

质数分解、因数数量、因数和、因数平均值、因数倒数和、因数积、111 的因数、因数分解、2的连续幂的积、等比数列

第6课

不同组合常⻅表达中结尾零的个数(比如阶乘)、n个物件的不同选法、模乘法、向下取整函数、2的连续幂的积

第7课

最小公倍数、最大公因数、质数分解、最大公因数和最小公倍数的乘积、最小公倍数和最大公因数的商、阶乘

第8课

辗转相除法和例子、斐波那契数列、111的因数、互质

第9课

互质、余数圈的性质、2、3、4、5、6、7、8、9倍数的余数、⻙恩图、容斥原理、欧拉函数

第10课

中国剩余定理与合数模运算、负余数、模运算方程组、最小公倍数、6和5倍数的余数、负余数

第11课

中国剩余定理与非互质数的模运算、9的倍数模12、模9的余数圈、最小公倍数、解模运算方程组、不可解的模运算方程组

第12课

模运算方程组、欧拉方程、模合数的余数、互质数、⻙恩图、因式分解、组合运算

第13课

因式分解、不同因数分解的总数、关于1/x的公式、0为什么不能做除数、一个等式的整数根数量

第14课

幂的余数、幂的余数圈、7的倍数末两位的规则、 7的倍数模4、幂的多次叠加

第15课

模运算里的倒数、整除7的规则及技巧、余数圈循环

第16课

有限小数和其分数形式、无限循环小数、为什么 √2 是无理数、质数分解、逻辑技巧和方向、反证法

高中生co-Star老师

Michelle Gao 的头像
MICHELLE GAO

马里兰大学数学竞赛Honorable Mention • 喜欢小提琴和排球,也喜欢物理和写码

点击查看更多

Razzi Masroor 的头像
RAZZI MASROOR

2020年俄亥俄州MATHCOUNTS州冠军, • 2022年和2023年均入选MOP(美国数学奥林匹克夏令营) • 麻省理工学院PRIMES Research Track

点击查看更多

退款政策

在学生的第一次LIVE课程结束后,将不接受退款请求;退款金额:按原付款方式退款90%,或按课程积分100%退款。