26.py

'''
Author:    Michael Sherif Naguib
Date:      November 2, 2019
@:         University of Tulsa

Question #26: 

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 __name__ =="__main__":
    '''
    My Analysis: 
        what makes this problem difficult or rather difficult to get accurate answers or efficient implementation ==>
        first thought is floating point errors and the fact that python the digit count is truncated ... 

        my pseudo code:
            calculate decimal representation
            count cycles 

    Initial Ideas:
        - powers of 5 and 2 never have repeating    
        - powers of 3 have an initial digit(s) then repete the same digit 
        - (Side note) ... was messing around dividing numbers and noticed 1/81 yeilds 0. 012345679 0123457 ... 
    '''