Project Euler 第26题

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

1/2 =0.5
1/3= 0.(3)
1/4=0.25
1/5=0.2
1/6=0.1(6)
1/7=0.(142857)
1/8= 0.125
1/9=0.(1)
1/10=0.1

Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.

找出大于1/1000的分数转换成小数后，循环位最长的数。

分数转换为小数，举例1/7

1. 1×10÷7=1余3

2. 3×10÷7=4余2

3. 2×10÷7=2余6

4. 6×10÷7=8余4

5. 4×10÷7=5余5

6. 5×10÷7=7余1

7.余数1重复，出现循环位。循环小数为0.(142857)

任何一个类似1/d（d为正整数）的分数，至多经过d次运算，一定会出现循环位。