def main():
lim = 1000
res = max_x = 0
squares = {x * x for x in range(2, int(sqrt(lim)) + 1)}
for d in range(2, lim + 1):
if d in squares:
continue
for num, den in convergent_fractions(quotients(d)):
if num * num - d * den * den == 1:
if num > max_x:
max_x, res = num, d
break
return res
def main():
# e = [2; 1,2,1, 1,4,1, 1,6,1, ...]
def quotients():
k = 2
yield k
while True:
yield from [1, k, 1]
k += 2
convergents = convergent_fractions(quotients())
for _ in repeat(None, 100):
num = next(convergents)[0]
return sum(map(int, str(num)))
def main():
lim = 1000
res = max_x = 0
squares = {x*x for x in range(2, int(sqrt(lim)) + 1)}
for d in range(2, lim+1):
if d in squares:
continue
for num, den in convergent_fractions(quotients(d)):
if num*num - d*den*den == 1:
if num > max_x:
max_x, res = num, d
break
return res