LIVE 160: 数论工具
2月22日起，每周六上午12:30–2:00 （您所在地当地时间）
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上午8:30，中国时间。
不知道课程是否合适？来挑战一下能力水平测试吧！
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
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
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