随笔分类 -  ACM---数论

摘要：GCDTime Limit: 2000/1000 MS (Java/Others)Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 812Accepted Submission(s): 363Problem DescriptionThe greatest common divisor GCD(a,b) of two positive integers a and b,sometimes written (a,b),is the largest divisor common to a and b,For example,( 阅读全文

摘要：Calculation 2Time Limit: 2000/1000 MS (Java/Others)Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 1750Accepted Submission(s): 727Problem DescriptionGiven a positive integer N, your task is to calculate the sum of the positive integers less than N which are not coprime to N. A is said 阅读全文

摘要：The Euler functionTime Limit: 2000/1000 MS (Java/Others)Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 2986Accepted Submission(s): 1221Problem DescriptionThe Euler function phi is an important kind of function in number theory, (n) represents the amount of the numbers which are smalle 阅读全文

摘要：欧拉函数：一个整数n，小于且和n互质的正整数的个数（包含1）的个数，用φ(n)表示。完全余数集合:欧拉函数中与n互质的数字的集合.~~~~~~~~~~~~~~性质：如果n是素数，则 φ(n)=n-1；求一个数n的所有互素和 sum=φ(n)*n/2; <==这个性质，很有用。欧拉定理：对于互质的正整数a和n，有aφ(n)≡1modn。费马定理：若正整数a与素数p互质，则有ap-1≡1modp。证明这个定理非常简单，由于φ(p)=p-1，代入欧拉定理即可证明。~~~~~~~~~~~~~~~~~~~~~~补充欧拉公式：1.pk的欧拉函数对于给定的一个素数p，φ(p)=p-1。则对于正整数n= 阅读全文

摘要：素数打表，总结了两种形式。一种是传统的在一个数组里进行标记，进行判断。一种是直接将素数放进一个数组里。 1 #include 2 #include 3 #include 4 5 6 int prime[1000003],size=0; 7 int s[1000003]; 8 9 void make_ini() //素数打表。直接装在一个数组里面10 {11 int i,j;12 memset(s,0,sizeof(s));13 for(i=2;i<=1000000;i++)14 {15 if(s[i]==0)16 {17 ... 阅读全文