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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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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EXAMPLE
| 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
| ok[x_] := Reduce[{y^2 == x^3 + x^2 - 9*x + 16, y >= 0}, y, Integers] =!= False; Select[Table[x, {x, -4, 10000}], ok ] (* From Jean-François Alcover, Sep 07 2011 *)
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PROG
| (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
| Cf. A117950, A132411, A132414, A002522, A028872.
Sequence in context: A144161 A054669 A131027 * A021236 A136590 A117026
Adjacent sequences: A133472 A133473 A133474 * A133476 A133477 A133478
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KEYWORD
| sign,full,fini
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AUTHOR
| Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 29 2007
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EXTENSIONS
| Edited by Max Alekseyev (maxale(AT)gmail.com), Nov 13 2009
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