new_contents: #!/usr/bin/env python
  #-*-coding:utf-8-*-
  
  '''
  The first ten continued fraction representations of (irrational) square roots are:
  
  √2=[1;(2)], period=1
  √3=[1;(1,2)], period=2
  √5=[2;(4)], period=1
  √6=[2;(2,4)], period=2
  √7=[2;(1,1,1,4)], period=4
  √8=[2;(1,4)], period=2
  √10=[3;(6)], period=1
  √11=[3;(3,6)], period=2
  √12= [3;(2,6)], period=2
  √13=[3;(1,1,1,1,6)], period=5
  
  Exactly four continued fractions, for N ≤ 13, have an odd period.
  
  How many continued fractions for N ≤ 10000 have an odd period?
  '''
  
  import math
  import timeit
  
  
  def make_proper(x, m, n):
      a = int(math.sqrt(x)+m)/n
      m -= a*n
      return a, m
  
  
  def inverse_rationalize(x, m, n):
      n = (x-m**2)/n
      return n, -m
  
  
  def calc(x, m, n):
      pairs = []
      while True:
          a, m = make_proper(x, m, n)
          n, m = inverse_rationalize(x, m, n)
          if [a, n, m] in pairs:
              return pairs[1:]
          else:
              pairs.append([a, n, m])
  
  
  def loop(n):
      odd_period = 0
      for i in range(1, n+1):
          if math.sqrt(i) == int(math.sqrt(i)):
              continue
          if len(calc(i, 0, 1))%2 == 1:
              odd_period += 1
      return odd_period
  
  
  if __name__ == '__main__':
      print loop(10000)
      print timeit.Timer('problem_064.loop(10000)', 'import problem_064').timeit(1)
  
subject: add problem 064