113 - Power of Cryptography

Power of Cryptography 

 

Background

Current work in cryptography involves (among other things) large prime numbers and computing powers of numbers modulo functions of these primes. Work in this area has resulted in the practical use of results from number theory and other branches of mathematics once considered to be of only theoretical interest.

This problem involves the efficient computation of integer roots of numbers.

 

The Problem

Given an integer  and an integer  you are to write a program that determines  , the positive root of p. In this problem, given such integers n and p, p will always be of the form  for an integerk (this integer is what your program must find).

 

The Input

The input consists of a sequence of integer pairs n and p with each integer on a line by itself. For all such pairs  ,  and there exists an integer k,  such that  .

 

The Output

For each integer pair n and p the value  should be printed, i.e., the number k such that  .

 

Sample Input

 

2
16
3
27
7
4357186184021382204544

 

Sample Output

 

4
3
1234

#include"stdio.h"
#include"math.h"
int main()
{
 double p,k;
 float n;
 while(scanf("%f\n%lf",&n,&p)!=EOF)
 {
 k=exp(log(p)/n);//用于计算题目要求的公式（该公式可使计算机识别更大数值的数字）；
 printf("%0.lf\n",k);
 }
 return 0;
}