points: 10 level: Medium title: Problem 5 author: Abhay Rana [email protected] answer: 161bc277c6df78ba8e05623fbece8a9728e08759
Consider the following fractions :
$1/4=0.25$ $1/3=0.\overline{3}$ $1/7=0.\overline{142857}$ $1/11=0.\overline{09}$ $1/17=0.\overline{0588235294117647}$
We notice that :
-
$1/4$ has a 0 digit recurring cycle -
$1/3$ has a 1 digit recurring cycle -
$1/7$ has a 6 digit recurring cycle -
$1/11$ has a 2 digit recurring cycle -
$1/17$ has a 16 digit recurring cycle.
Find the sum of all numbers N below 1000, for which 1 / N contains a recurring cycle of more than 25 digits.