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Reciprocal cycles

Problem 26

Published on 13 September 2002 at 06:00 pm [Server Time]

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.


Answer:
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