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.
If 1/n repeats after d digits, then 10d is equivalent to 1 modulo n. (just be sure to find the smallest such d)
...
Well, that didn't work. It turns out that that statement is only true for numbers where 1/n starts repeating immediately. Fortunately, a related equation is true:
(10^k) % n == (10^(k + d)) % n
for k >= n. No real rust issues this time around, just tying myself
into infinite loops.