NOTE: Spoilers below!

Idea:

if 10 is a primitive root mod p, then cycle is p-1. start at 997 and check.

resources:

http://en.wikipedia.org/wiki/Repeating_decimal http://primes.utm.edu/lists/small/1000.txt http://dbfin.com/2012/04/primitive-roots-modulo-the-first-1000-numbers/

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The solution runs in and returns the answer .