数论工具
LIVE系列课程中最具挑战性的模块，是对数论中抽象概念的系统介绍。通过精心设计和挑选的题目来讲解数论主题，使抽象晦涩的思考变得更加容易理解。该课程难度范围覆盖MATHCOUNTS、AMC 8 和 AMC 10、AMC 12、AIME。
想了解我们独具一格的教学方法？欢迎您访问我们的主页，看看我们是如何打破线上数学课的固定框架的吧！
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这门课适合我吗？
你是否正在上从6年级数学到微积分的数学课程，并且已经了解组合课程中的内容？如果是的话，你已经具备了足够的能力来加入这门课。这门课将带你高效学习如何理解学校课本里并不教授，但却极具挑战性的数论概念。
不知道课程是否合适？来挑战一下能力水平测试吧！
课程结构
每个模块的课程均包含20节LIVE课程，分为16节【日挑战】课程和4节【单元考核测验】复习课程（学生需要在复习课前进入配套的Pre-Recorded课程完成测验）。每节课程都将由2位 Stars 共同授课。在该模块的学习中，我们将讨论超过150个数学问题。
【日挑战课程】每节课中，学生都会学习解决全新的数学问题，老师们将通过启发式的教学引导和鼓励学生开创自己的解题方法。我们的LIVE课堂赞赏学生们提出自己的想法，鼓励每个学生和全班同学一起集思广益，构建各种不同的解题方法，更积极地参与数学发现。
【单元考核测验】包含20道数学问题，其中10题在正常难度范围内，而另外10题则非常具有挑战性。
学生评价
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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.
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!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
课程大纲
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
报名课程
每位报名LIVE在线直播课的学生都将同时享有对应的Pre-Recorded自学录播课程一年使用权，无需额外购买。LIVE直播课经过罗教授和教学团队精心设计的，通过前所未有的引人入胜的教学方式、极为丰富的课堂交互体验，让学生在趣味学习中爱上挑战和思考。 以下所有直播课显示时间均为您的当地时间（美国将于2023年3月12日星期日进入夏令时，请其他国家和地区的学生注意课程时间调整）。
如果你有强大的自驱力可以进行自主学习，或者想比LIVE课程安排更快地完成一个模块的学习，也欢迎你选择我们的自学录播课程。录播课包含了所有罗教授关于该模块的教学视频（没有直播课堂），在过去3年中也有数千名来自世界各地的同学参与学习。