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Pythagorean triples: Difference between revisions
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Up to a perimeter of 19500 there are 10388 triples, of which 1373 are primitive
Up to a perimeter of 20000 there are 10689 triples, of which 1408 are primitive</pre>
Barebone minimum for this task:<lang Python>from sys import setrecursionlimit
setrecursionlimit(2000) # 2000 ought to be big enough for everybody
def triples(lim, a = 3, b = 4, c = 5):
l = a + b + c
if l > lim: return (0, 0)
return reduce(lambda x, y: (x[0] + y[0], x[1] + y[1]), [
(1, lim / l),
triples(lim, a - 2*b + 2*c, 2*a - b + 2*c, 2*a - 2*b + 3*c),
triples(lim, a + 2*b + 2*c, 2*a + b + 2*c, 2*a + 2*b + 3*c),
triples(lim, -a + 2*b + 2*c, -2*a + b + 2*c, -2*a + 2*b + 3*c) ])
for peri in [10 ** e for e in range(1, 8)]:
print peri, triples(peri)</lang>Output:<lang>10 (0, 0)
100 (7, 17)
1000 (70, 325)
10000 (703, 4858)
100000 (7026, 64741)
1000000 (70229, 808950)
10000000 (702309, 9706567)</lang>
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