Problem 26

Problem 26

13 September 2002

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.

如果d只有2和5两个约数，则没有¹/_d循环小数，如果d还有其他的约数，则¹/_d的循环小数的长度和d除去其所有2和5的约数的值d1的循环小数长度相同，比如6就和3的循环小数长度相同

def fun26():
    result = (0,0)
    for i in range(2, 1000):
        print i
        while i%2 == 0:
            i /= 2
        while i%5 == 0:
            i /= 5
        if i == 1:
            continue

        count  = 9
        length = 1
        while 1:
            if count%i == 0:
                if length > result[0]:
                    result = (length, i)
                break
            else:
                count   = count*10 + 9
                length += 1
    return result

answer is 983, the length of recurring cycle is 982