Project Euler Problem 26

問題

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.

ソース

max = 1000
prime = Array.new(max, 1)
prime[0..1] = [0, 0]
i = 2
while i < Math.sqrt(max).to_i + 1 do
	(i + i).step(max, i){|x| prime[x] = 0}
	i += prime[(i + 1)..max].index(1) + 1
end

puts prime.each_index{|i|
	prime[i] = i unless prime[i].zero?
}.select{|x| !x.zero?}.map{|x|
	i = 1
	while true
		r = (10 ** i) % x
		break if r == 1 || r == 0
		i += 1
	end
	[x, r == 0 ? 0 : i]
}.sort{|a, b| b[1] <=> a[1]}[0][0]

解答

983

感想

フェルマーの小定理なんて使うんや。。。
そういえば大学のときやったような、やっていないような。。。

参考

http://www3.ocn.ne.jp/~fukiyo/math-obe/fermat.htm