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The branch of mathematics called number theory is about properties of numbers. One of the areas that has captured the interest of number theoreticians for thousands of years is the question of primality. A prime number is a number that is has no proper fac

素数

poj 2992 Divisors 筛法 算术基本定理Your task in this problem is to determine the number of divisors of Cnk. Just for fun -- or do you need any special reason for such a useful computation?

poj 2262 Goldbach's Conjecture 筛法 哥德巴赫猜想In 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 written as the sum of two odd prime n

poj 2191 Mersenne Composite Numbers 筛法判素数One of the world-wide cooperative computing tasks is the "Grand Internet Mersenne Prime Search" -- GIMPS -- striving to find ever-larger prime numbers by examining a particular category of such numbers.

hdu 2710 Max Factor 筛法To improve the organization of his farm, Farmer John labels each of his N (1 <= N <= 5,000) cows with a distinct serial number in the range 1..20,000. Unfortunately, he is unaware that the cows interpret some serial numbers as better

poj 1730 Perfect Pth Powers 筛法We say that x is a perfect square if, for some integer b, x = b2. Similarly, x is a perfect cube if, for some integer b, x = b3. More generally, x is a perfect pth power if, for some integer b, x = bp. Given an integer x you

poj 1142 Smith Numbers 筛法While skimming his phone directory in 1982, Albert Wilansky, a mathematician of Lehigh University,noticed that the telephone number of his brother-in-law H. Smith had the following peculiar property: The sum of the digits of that

hdu 4715 Difference Between Primes 筛法All you know Goldbach conjecture.That is to say, Every even integer greater than 2 can be expressed as the sum of two primes. Today, skywind present a new conjecture: every even integer can be expressed as the differen

hdu 1286 找新朋友 欧拉函数新年快到了，“猪头帮协会”准备搞一个聚会，已经知道现有会员N人，把会员从1到N编号，其中会长的号码是N号，凡是和会长是老朋友的，那么该会员的号码肯定和N有大于1的公约数，否则都是新朋友，现在会长想知道究竟有几个新朋友？请你编程序帮会长计算出来。

哥德巴赫猜想大家都知道一点吧.我们现在不是想证明这个结论,而是想在程序语言内部能够表示的数集中,任意取出一个偶数,来寻找两个素数,使得其和等于该偶数.做好了这件实事,就能说明这个猜想是成立的.由于可以有不同的素数对来表示同一个偶数,所以专门要求所寻找的素数对是两个值最相近的.

poj 3842 An Industrial Spy 筛法 全排列DescriptionIndustrial spying is very common for modern research labs. I am such an industrial spy - don't tell anybody! My recent job was to steal the latest inventions from a famous math research lab. It was hard to obta