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A308395
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Numbers y such that x*(x+1) + y*(y+1) = z*(z+1) is solvable in positive integers x, z with x <= y.
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2
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2, 5, 6, 9, 10, 13, 14, 17, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 35, 37, 38, 39, 41, 42, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 61, 62, 65, 66, 68, 69, 70, 73, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 89, 90, 91, 92, 93, 94, 95, 97
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OFFSET
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1,1
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LINKS
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EXAMPLE
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14 is a term because 14*15 + 14*15 = 20*21.
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MATHEMATICA
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max = 220; lst = {}; For[x = 1, x < max, x++,
For[y = x, y < max, y++,
For[z = y, z < max, z++,
If[x (x + 1) + y (y + 1) == z (z + 1),
lst = AppendTo[lst, y]]]]]; Select[Union[lst], # < max/2 &]
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PROG
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(Python)
from sympy import integer_nthroot
w += y
z = 0
for x in range(1, y+1):
z += x
if integer_nthroot(8*(w+z)+1, 2)[1]:
break
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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