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Search: id:A133475
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| A133475 |
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Integers n such that n^3 + (n - 5)^2 + n - 9 is a square. |
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+0
1
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| -4, -3, -1, 0, 1, 3, 5, 11, 15, 28, 47, 55, 81, 549, 1799, 8361
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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n^3 + (n - 5)^2 + n - 9 = n^3 + n^2 - 9*n + 16. The set of x values of integral solutions to the elliptic curve y^2 = n^3 + n^2 - 9*n + 16 (see MAGMA program) is { -4, -3, -1, 0, 1, 3, 5, 11, 15, 28, 47, 55, 81, 549, 1799, 8361 }
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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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MAPLE
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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)) ])};
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CROSSREFS
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Cf. A132410, A132411, A132414, A002522, A028872.
Adjacent sequences: A133472 A133473 A133474 this_sequence A133476 A133477 A133478
Sequence in context: A010102 A054669 A131027 this_sequence A021236 A136590 A117026
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KEYWORD
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sign
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AUTHOR
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Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 29 2007
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