def main():
max_d, max_x = 0, 0
for d in xrange(2, 1001):
for x, y in continued_fraction(d):
if x ** 2 - d * y ** 2 == 1:
if x > max_x:
max_x = x
max_d = d
break
print max_d
def solve_diophantine_equation(D):
n = 0
expansion = continued_fraction(D)
while True:
frac = approximation(expansion, n)
x = frac.numerator
y = frac.denominator
if x**2 - D * y**2 == 1:
return x, y
break
n += 1
def main():
print sum(
[1 for i in [max(0, len([i for i in continued_fraction(n, True)]) - 1) for n in xrange(2, 10001)] if i % 2 == 1]
)
