Alex_McAvoy的博客

【概述】判断素数是一个较常涉及的内容，所谓素性测试是检测一个数是否为素数的测试。素数定理：，其中 π(x) 表示不超过 x 的素数的个数质数分布密度定理：素数的分布越来越稀疏，当 1E18 内的任意两个素数的差不会很大（不会超过 300）【埃拉托斯特尼筛法】初始时，先假设所有数都是素数，从2开始枚举，当找到一个素数时，显然这个素数乘上另外一个数之后都是合数，把这些合数都筛掉，继...

Problem DescriptionYou are given a positive integer n > 1. Consider all the different prime divisors of n. Each of them is included in the expansion n into prime factors in some degree. Required...

Problem DescriptionA prime number is a natural number greater than 1 and has exactly 2 divisors which are 1 and the number itself.You are given a prime number nn, find any 2 prime numbers aa and ...

Problem DescriptionYou've decided to carry out a survey in the theory of prime numbers. Let us remind you that a prime number is a positive integer that has exactly two distinct positive integer di...

题目背景1742年6月7日哥德巴赫写信给当时的大数学家欧拉，正式提出了以下的猜想：任何一个大于9的奇数都可以表示成3个质数之和。质数是指除了1和本身之外没有其他约数的数，如2和11都是质数，而6不是质数，因为6除了约数1和6之外还有约数2和3。需要特别说明的是1不是质数。这就是哥德巴赫猜想。欧拉在回信中说，他相信这个猜想是正确的，但他不能证明。从此，这道数学难题引起了几乎所有数学家的...

Problem DescriptionThe sequence of n − 1 consecutive composite numbers (positive integers that are not prime and not equal to 1) lying between two successive prime numbers p and p + n is called a p...

Problem DescriptionSome positive integers can be represented by a sum of one or more consecutive prime numbers. How many such representations does a given positive integer have? For example, the in...

【题目描述】现在处女座顺利的完成了测验，处女座想要知道知道自己输出的结果是否正确。他希望知道自己有自己输出的数中有多少对是不满足要求的。更具体的，处女座想知道下面程序段的答案int main(){ int n; cin>>n; for(int i=1;i<=n;i++) cin>>a[i]; int a...

【题目描述】处女座进行了一场 c 语言的考试，要求很简单，输出2000个正整数，并且满足以下条件：1.任意两个数互质2.任意两个数 x,y，满足 τ(x*y)>10，其中为 n 的因子的个数举例：6的因子有1，2，3，6，所以 τ(6)=4【输入描述】本题没有输入【输出描述】2000行，每行一个正整数输出的每个整数都必须在1-4*10^8之间如果有多组...

Problem DescriptionBamboo Pole-vault is a massively popular sport in Xzhiland. And Master Phi-shoe is a very popular coach for his success. He needs some bamboos for his students, so he asked his a...

Problem DescriptionA string ss of length nn can be encrypted by the following algorithm:iterate over all divisors of nn in decreasing order (i.e. from n to 1),for each divisor dd, reverse the su...

Problem DescriptionA prime number is a counting number (1, 2, 3, ...) that is evenly divisible only by 1 and itself. In this problem you are to write a program that will cut some number of prime nu...

Problem DescriptionGoldbach's Conjecture: For any even number n greater than or equal to 4, there exists at least one pair of prime numbers p1 and p2 such that n = p1 + p2.This conjecture has not...

Problem DescriptionIn 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture:Every even number greater than 4 can be...

Problem DescriptionFermat's theorem states that for any prime number p and for any integer a > 1, ap = a (mod p). That is, if we raise a to the pth power and divide by p, the remainder is a. Som...

题目描述因为151既是一个质数又是一个回文数(从左到右和从右到左是看一样的)，所以 151 是回文质数。写一个程序来找出范围[a,b](5 <= a < b <= 100,000,000)( 一亿)间的所有回文质数;输入输出格式输入格式：1 行: 二个整数 a 和 b .输出格式：输出一个回文质数的列表，一行一个。输入输出样例输入样例#1：...

Problem DescriptionFor a positive integern, let's denote functionf(n,m)as them-th smallest integerxthatx>nandgcd(x,n)=1. For example,f(5,1)=6andf(5,5)=11.You are given the value of...