## Reciprocal cycles

### Problem 26

Published on Friday, 13th September 2002, 06:00 pm; Solved by 36089

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.