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A133475
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Integers n such that n^3 + n^2 - 9*n + 16 is a square.
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0
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-4, -3, -1, 0, 1, 3, 5, 11, 15, 28, 47, 55, 81, 549, 1799, 8361
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OFFSET
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1,1
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COMMENTS
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The set of x values of integral points on the elliptic curve y^2 = x^3 + x^2 - 9*x + 16.
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LINKS
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EXAMPLE
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0^3 + (-5)^2 + (-9) = 4^2, 1^3 + (-4)^2 + (-8) = 3^2, 3^3 + (-2)^2 + (-6) = 5^2
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MATHEMATICA
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ok[x_] := Reduce[{y^2 == x^3 + x^2 - 9*x + 16, y >= 0}, y, Integers] =!= False; Select[Table[x, {x, -4, 10000}], ok ] (* Jean-François Alcover, Sep 07 2011 *)
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PROG
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(Magma) P<n> := PolynomialRing(Integers()); {x: x in Sort([ p[1] : p in IntegralPoints(EllipticCurve(n^3 + n^2 - 9*n + 16)) ])};
(Sage) EllipticCurve([0, 1, 0, -9, 16]).integral_points()
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CROSSREFS
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KEYWORD
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sign,full,fini
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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