The group of Absurd Calculation Maniacs has discovered a great new way how to count. Instead of using the ordinary decadic numbers, they use Fibonacci base numbers. Numbers in this base are expressed as sequences of zeros and ones similarly to the binary numbe…
题意： 给你一个n，求所有gcd(i , j)的和，其中1 <= i < j <= n。 题解： 我们假设gcd[n]表示1到n-1与n的gcd的和，那么s[n]=s[n-1]+gcd[n]; phi[i]表示与gcd（n, x）= i 的x的个数；gcd[n]=sum( phi[i] * i ) , 所以我们只需求phi[i]即可；根据gcd(n, x)=i ----->gcd(n/i, x/i) = 1, 因此仅仅要求出欧拉函数phi(n / i)，就能够得到与n / i互质的个数，从而…
We all know the Super Powers of this world and how they manage to get advantages in political warfare or even in other sectors. But this is not a political platform and so we will talk about a different kind of super powers — “The Super Power Numbers”. A posit…
Euler is a well-known matematician, and, among many other things, he discovered that the formula n^2 + n + 41 produces a prime for 0 ≤ n < 40. For n = 40, the formula produces 1681, which is 41 × 41. Even though this formula doesn’t always produce a prime, …
Given the N integers, you have to nd the maximum GCD (greatest common divisor) of every possible pair of these integers. Input The rst line of input is an integerN(1<N<100) that determines the number of test cases. The followingNlines are theNtest cases.…
Find the result of the following code: long long pairsFormLCM( int n ) { long long res = 0; for( int i = 1; i A straight forward implementation of the code may time out. If you analyze the code, you will find that the code actually counts the number of pairs (…
Dr. Mob has just discovered a Deathly Bacteria. He named it RC-01. RC-01 has a very strange reproduction system. RC-01 lives exactly x days. Now RC-01 produces exactly p new deadly Bacteria where x = b^p (where b, p are integers). More generally, x is a perfec…
A Compiler Mystery: We are given a C-language style for loop of type for (variable = A; variable != B; variable += C) statement; I.e., a loop which starts by setting variable to value A and while variable is not equal to B, repeats statement followed by increa…
Write a program to read in a list of integers and determine whether or not each number is prime. A number, n, is prime if its only divisors are 1 and n. For this problem, the numbers 1 and 2 are not considered primes. Input Each input line contains a single in…
两只青蛙在网上相识了，它们聊得很开心，于是觉得很有必要见一面。它们很高兴地发现它们住在同一条纬度线上，于是它们约定各自朝西跳，直到碰面为止。可是它们出发之前忘记了一件很重要的事情，既没有问清楚对方的特征，也没有约定见面的具体位置。不过青蛙们都是很乐观的，它们觉得只要一直朝着某个方向跳下去，总能碰到对方的。但是除非这两只青蛙在同一时间跳到同一点上，不然是永远都不可能碰面的。为了帮助这两只乐观的青蛙，你被要求写一个程序来判断这两只青蛙是否能够碰面，会在什么时候碰面。 我们把这两只青蛙分别叫做青蛙A和青蛙B，并且规定纬度…
