https://baike.baidu.com/item/模反元素/20417595 如果两个正整数a和n互质,那么一定可以找到整数b,使得 ab-1 被n整除,或者说ab被n除的余数是1.这时,b就叫做a的“模反元素” 中文名 模反元素 外文名modulo multiplicative inverse 同义词 模逆元素 如果两个正整数a和n互质,那么一定可以找到整数b,使得 ab-1 被n整除,或者说ab被n除的余数是1. 这时,b就叫做a对模数n的“模反元素”.比如,3和11互质,那么3的模…

https://en.wikipedia.org/wiki/Euler's_totient_function counts the positive integers up to a given integer n that are relatively prime to n. if two numbers m and n are relatively prime, then φ(mn) = φ(m) φ(n); https://zh.wikipedia.org/wiki/同餘 数学上,同余(英…

链接:http://acm.hdu.edu.cn/showproblem.php?pid=6322 Problem Description In number theory, Euler's totient function φ(n) counts the positive integers up to a given integer n that are relatively prime to n . It can be defined more formally as the number…

GTW likes function 题目连接: http://acm.hdu.edu.cn/showproblem.php?pid=5596 Description Now you are given two definitions as follows. f(x)=∑xk=0(−1)k22x−2kCk2x−k+1,f0(x)=f(x),fn(x)=f(fn−1(x))(n≥1) Note that φ(n) means Euler's totient function.(φ(n)is an…

题目链接: GTW likes function Time Limit: 4000/2000 MS (Java/Others)     Memory Limit: 131072/131072 K (Java/Others) Problem Description   Now you are given two definitions as follows. f(x)=∑xk=0(−1)k22x−2kCk2x−k+1,f0(x)=f(x),fn(x)=f(fn−1(x))(n≥1) Note th…

题目链接 和上面几题差不多的 Euler's Totient function, φ(n) [sometimes called the phi function]:小于等于n的数并且和n是互质的数的个数 存在这样的数:N的欧拉数φ(n),是N的一个排列 例如:φ(87109)=79180 求在1---10^7中n/φ(n) 取到最小的 n 是多少? 这里的是p是n的素因子,当素因子有相同的时候只取一个 任意一个正整数都能分解成若干个素数乘积的形式 直接利用上题的phi函数就可以求解 这个是跑的最…

Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relative…

题目链接: https://projecteuler.net/problem=516 题目: \(5\)-smooth numbers are numbers whose largest prime factor doesn't exceed \(5\). \(5\)-smooth numbers are also called Hamming numbers. Let S(L) be the sum of the numbers \(n\) not exceeding \(L\) such t…

http://www.cppblog.com/RyanWang/archive/2009/07/19/90512.aspx?opt=admin 欧拉函数 E(x)表示比x小的且与x互质的正整数的个数.*若p是素数,E(p)=p-1.*E(pk)=pk-pk-1=(p-1)*pk-1证:令n=pk,小于n的正整数数共有n-1即(pk-1)个,其中与p不质的数共[pk-1-1]个(分别为1*p,2*p,3*p...p(pk-1-1)).所以E(pk)=(pk-1)-(pk-1-1)=pk-pk-1.…

51Nod: http://www.51nod.com/onlineJudge/questionCode.html#!problemId=1136 1136 欧拉函数 基准时间限制:1 秒 空间限制:131072 KB 分值: 0 难度:基础题   对正整数n,欧拉函数是少于或等于n的数中与n互质的数的数目.此函数以其首名研究者欧拉命名,它又称为Euler's totient function.φ函数.欧拉商数等.例如:φ(8) = 4(Phi(8) = 4),因为1,3,5,7均和8互质.  …