Euler theorem 思路:找规律 a       余数                  个数 1       0 1                     2 2       0 2                     2 3       0 1 3                  3 4       0 1 4                  3 5       0 1 2 5               4 6       0 1 2 6               4…

HazelFan is given two positive integers a,b, and he wants to calculate amodb. But now he forgets the value of b and only remember the value of a, please tell him the number of different possible results. Input The first line contains a positive integ…

6322.Problem D. Euler Function 题意就是找欧拉函数为合数的第n个数是什么. 欧拉函数从1到50打个表,发现规律,然后勇敢的水一下就过了. 官方题解: 代码: //1004-欧拉函数水题 #include<iostream> #include<cstdio> #include<cstring> #include<algorithm> #include<cmath> using namespace std; typede…

题目链接:hdu 2824 The Euler function 题意: 让你求一段区间的欧拉函数值. 题解: 直接上板子. 推导过程: 定义:对于正整数n,φ(n)是小于或等于n的正整数中,与n互质的数的数目. 例如:φ(8)=4,因为1,3,5,7均和8互质. 性质:1.若p是质数,φ(p)= p-1. 2.若n是质数p的k次幂,φ(n)=(p-1)*p^(k-1).因为除了p的倍数都与n互质 3.欧拉函数是积性函数,若m,n互质,φ(mn)= φ(m)φ(n). 根据这3条性质我们就可以推…

Problem Description HazelFan is given two positive integers a,b, and he wants to calculate amodb. But now he forgets the value of b and only remember the value of a, please tell him the number of different possible results.   Input The first line con…

Problem Description 我知道部分同学最近在看中国剩余定理,就这个定理本身,还是比较简单的: 假设m1,m2,-,mk两两互素,则下面同余方程组: x≡a1(mod m1) x≡a2(mod m2) - x≡ak(mod mk) 在0<=<m1m2-mk内有唯一解. 记Mi=M/mi(1<=i<=k),因为(Mi,mi)=1,故有二个整数pi,qi满足Mipi+miqi=1,如果记ei=Mi/pi,那么会有: ei≡0(mod mj),j!=i ei≡1(mod m…

Infinite monkey theorem Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)http://acm.hdu.edu.cn/showproblem.php?pid=3689 Problem Description Could you imaging a monkey writing computer programs? Surely monkeys are sma…

The Euler function Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 5028    Accepted Submission(s): 2123 Problem Description The Euler function phi is an important kind of function in number theo…

Infinite monkey theorem Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 1702 Accepted Submission(s): 882 Problem Description Could you imaging a monkey writing computer programs? Surely monkeys are…

//题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=6322 //题目大意:给定 k,求第 k 小的数 n,满足 φ(n) 是合数.显然 φ(1) = 1 不是合数,只考虑 n ≥ 2 的情况.//思路:得到题意之后,查到了一张表(https://en.wikipedia.org/wiki/Euler%27s_totient_function)//得知当且仅当 n = 1, 2, 3, 4, 6 时,φ(n) 不是合数.第1小的K值是5,第二小的K值…