Project Euler 题解 #63 Powerful digit counts

题目：Powerful digit counts

The 5-digit number, 16807=7⁵, is also a fifth power. Similarly, the 9-digit number, 134217728=8⁹, is a ninth power.

How many n-digit positive integers exist which are also annth power?

 

分析

假设一个位数为x的数S=k^x,得到关系式：

 

右端可得：1<=k<=9

左端看得：k>=10^1-1/x,

题目的解就是统计满足上面不等式的k值的总数。

列图表解：

结果为49.