def answer():
count = 0
for n in range(2, 10001):
if is_square(n):
continue
if len(square_continued(n))%2:
count += 1
return count
def solve_pells(num):
if is_square(num):
return 0
# b_n is found by square_continued and a_n is always 1
guess = int(num**0.5)
b = square_continued(num)
#A_1 and B_1 given by A_1/B_1 = ((b1*b0) + a1)/b1
numerator = [guess, guess*b[0] + 1]
denominator = [1, b[0]]
if numerator[1]**2 - num*denominator[1]**2 == 1:
return numerator[1]
for n in itertools.count(2):
# A_n = b_n * A_n-1 + a_n* A_n-2 where A_n is approx numerator
# B_n = b_n * B_n-1 + a_n* A_n-2 where B_n is approx denominator
x = b[(n-1)%len(b)] * numerator[n-1] + numerator[n-2]
y = b[(n-1)%len(b)] * denominator[n-1] + denominator[n-2]
if x**2 - num*y**2 == 1:
return x
numerator.append(x)
denominator.append(y)