使用double处理大整数&泰勒公式与误差分析
113 - Power of Cryptography
Time limit: 3.000 seconds
http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=99&page=show_problem&problem=49
http://poj.org/problem?id=2109
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
题意：给出n和p，求出 ，但是p可以很大（）
如何存储p？不用大数可不可以？
先看看double行不行：指数范围在-307~308之间(以10为基数)，有效数字为15位。
误差分析：
令f(p)=p^(1/n)，Δ=f(p+Δp)-f(p)
则由泰勒公式得
（Δp的上界是因为double的精度最多是15位，n有下界是因为 ）
由上式知，当Δp最大，n最小的时候误差最大。
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