59 lines
1.5 KiB
Python
59 lines
1.5 KiB
Python
#!/usr/bin/env python3
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from collections import defaultdict
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from math import gcd
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def sols(N):
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"""yields solutions of x**2 + 3y**2 = z**2 where x + y <= 2N"""
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for l in range(1, N+1, 2):
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for k in range(1, N//l + 1, 2):
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if gcd(l, k) != 1:
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continue
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x = abs(3*l**2 - k**2) // 2
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y = l * k
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z = (3*l**2 + k**2) // 2
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for n in range(1, (2*N) // (x+y) + 1):
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yield (n*x, n*y, n*z)
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for l in range(1, N//2 + 1):
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for k in range(1 + (l%2), N//(2*l) + 1, 2):
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if gcd(l, k) != 1:
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continue
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x = 2 * abs(3*l**2 - k**2)
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y = 4 * l * k
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z = 2 * (3*l**2 + k**2)
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if x + y > 2*N:
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continue
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for n in range(1, (2*N) // (x+y) + 1):
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yield (n*x, n*y, n*z)
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def pq_gen(N):
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"""yields solutions of c**2 = p**2 + q**2 + pq where c is int and p + q <= N"""
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for x, y, z in sols(N):
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p = y
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if x <= p or (x - p) % 2 != 0:
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continue
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q = (x - p) // 2
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yield p, q
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def find_pqr(N):
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pqs = defaultdict(lambda : set())
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for p, q in pq_gen(N-1):
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pqs[p].add(q)
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pqs[q].add(p)
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sums = set()
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for p, qrs in dict(pqs).items():
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for q in qrs:
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for r in qrs:
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if p + q + r > N or r not in pqs[q]:
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continue
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sums.add(p + q + r)
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return sum(sums)
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N = 120 * 1000
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print(find_pqr(N))
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