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66.py
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66.py
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# Diophantine equation
from utils import continued_fraction, is_square
from fractions import Fraction
def approximation(expansion, n):
a0 = expansion[0]
a1 = expansion[1:]
frac = Fraction(0)
l = len(expansion) - 1
for i in range(n-1, -1, -1):
frac = 1/(a1[i%l] + frac)
return a0 + frac
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
x_max = 0
D_max = 0
for D in range(1000):
if is_square(D):
continue
x,y = solve_diophantine_equation(D)
if x > x_max:
x_max = x
D_max = D
print D_max