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A237351
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Positive integers k such that x^2 - 5xy + y^2 + k = 0 has integer solutions.
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11
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3, 5, 12, 17, 20, 21, 27, 35, 41, 45, 47, 48, 59, 68, 75, 80, 83, 84, 89, 101, 108, 111, 119, 125, 129, 131, 140, 147, 153, 164, 167, 173, 180, 185, 188, 189, 192, 201, 215, 227, 236, 237, 243, 245, 251, 255, 257, 269, 272, 287, 293, 300, 311, 315, 320, 327
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OFFSET
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1,1
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COMMENTS
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See comments on method used in A084917.
The equivalent sequence for x^2 - 3xy + y^2 + k = 0 is A031363.
The equivalent sequence for x^2 - 4xy + y^2 + k = 0 is A084917.
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LINKS
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EXAMPLE
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12 is in the sequence because x^2 - 5xy + y^2 + 12 = 0 has integer solutions, for example, (x, y) = (2, 8).
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MATHEMATICA
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Select[Range[350], Length[FindInstance[x^2-5x y+y^2+#==0, {x, y}, Integers]]>0&] (* Harvey P. Dale, Apr 23 2023 *)
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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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