X-factor Chains

Given a positive integer X, an X-factor chain of length m is a sequence of integers, 1 = X0, X1, X2, …, Xm = X satisfying Xi < Xi+1 and Xi | Xi+1 where a | b means a perfectly divides into b. Now we are interested in the maximum >>继续阅读

Longge's problem

Longge is good at mathematics and he likes to think about hard mathematical problems which will be solved by some graceful algorithms. Now a problem comes: Given an integer N(1 < N < 2^31),you are to calculate ∑gcd(i, N) 1< >>继续阅读

Sumdiv

Consider two natural numbers A and B. Let S be the sum of all natural divisors of A^B. Determine S modulo 9901 (the rest of the division of S by 9901).

Input

The only line contains the two natural numbers A and B, (0 <= A,B <= 5000 >>继续阅读

Prime Land

Everybody in the Prime Land is using a prime base number system. In this system, each positive integer x is represented as follows: Let {pi}i=0,1,2,... denote the increasing sequence of all prime numbers. We know that x > 1 can be rep >>继续阅读

Eddy's research I

Problem Description

Eddy's interest is very extensive, recently he is interested in prime number. Eddy discover the all number owned can be divided into the multiply of prime number, but he can't write program, so Eddy has to as >>继续阅读

1215 - Finding LCM

You will be given a, b and L. You have to find c such that LCM (a, b, c) = L. If there are several solutions, print the one where c is as small as possible. If there is no solution, report so.LCM is an abbreviation used for Least >>继续阅读

1054 - Efficient Pseudo Code

pseudo codeSometimes it's quite useful to write pseudo codes for problems. Actually you can write the necessary steps to solve a particular problem. In this problem you are given a pseudo code to solve a problem and you >>继续阅读

1035 - Intelligent Factorial Factorization

Input

Given an integer N, you have to prime factorize N! (factorial N).

Input starts with an integer T (≤ 125), denoting the number of test cases.

Each case contains an integer N (2 ≤ N ≤ 100).

Out >>继续阅读