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.

解析：费马小定理的应用

def recu_cycle(d):
	for t in range(1,d):
		if 1 == 10**t % d:
			return t;
	return 0
longest = max(recu_cycle(i) for i in range(2,1001))
print [i for i in range(2,1001) if recu_cycle(i) == longest][0]