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- #!/usr/bin/python
- # Asymmetric Diophantine Equation
- # https://projecteuler.net/problem=764
- from math import isqrt
- from sympy import gcd
- def generate_solutions(N):
- solutions = set()
- for y in range(1, isqrt(N) + 1):
- y_squared = y**2
- for x in range(1, isqrt(N // 4) + 1):
- x_squared = 16 * x**2
- z_squared = x_squared + y_squared**2
- z = isqrt(z_squared)
- if z**2 == z_squared and z <= N and gcd([x, y, z]) == 1:
- solutions.add((x, y, z))
- return solutions
- def S(N):
- solutions = generate_solutions(N)
- return sum(sum(solution) for solution in solutions) % 10**9
- # Calculate S(10^16) mod 10^9
- result = S(10**4) #=> 702 (wrong)
- print(result)
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