37 lines
755 B
Python
37 lines
755 B
Python
#!/usr/bin/env python3
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from math import gcd
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def sols():
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"""yields solutions to a**2 - 2b**2 = -1"""
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a, b = 3, 2
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while True:
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yield 2*b - a, a - b
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a, b = 3*a + 4*b, 2*a + 3*b
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def mn_from_ab(a, b, sgn):
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M, N = a + b, b - sgn
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div = gcd(M, N)
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m, n = M // div, N // div
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return m, n
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def gen_mn(N):
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for a, b in sols():
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if b > N//2:
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break
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yield mn_from_ab(a, b, 1)
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yield mn_from_ab(a, b, -1)
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def is_primitive(m, n):
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return (m + n) % 2 == 1 and n != 0
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def count_triangles(m, n, circ):
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sides = (m**2 - n**2, 2*m*n, m**2 + n**2)
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return (circ-1) // sum(sides)
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N = 100 * 10**6
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R = sum(count_triangles(m, n, N) for m, n in gen_mn(N) if is_primitive(m, n))
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print(R)
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