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Search: id:A132414
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| A132414 |
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Natural integers n such that n^3 - (n + 2)^2 + n + 4 is a square. |
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+0
4
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OFFSET
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1,3
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COMMENT
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n^3 - (n + 2)^2 + n + 4 = n^3 - n^2 - 3*n. The set of x values of integral solutions to the elliptic curve y^2 = n^3 - n^2 - 3*n (see MAGMA program) is {-1, 0, 3, 4, 75}. - Klaus Brockhaus, Nov 13 2007
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EXAMPLE
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0^3 - 2^2 + 4 = 0^2, 3^3 - 5^2 + 7 = 3^2, 4^3 - 6^2 + 8 = 6^2 and 75^3 - 77^2 + 79 = 645^2.
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PROGRAM
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(MAGMA) P<n> := PolynomialRing(Integers()); {x: x in Sort([ p[1] : p in IntegralPoints(EllipticCurve(n^3 - n^2 - 3*n)) ])}; /* Klaus Brockhaus, Nov 13 2007 */
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CROSSREFS
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Cf. A028560, A005563.
Adjacent sequences: A132411 A132412 A132413 this_sequence A132415 A132416 A132417
Sequence in context: A052323 A012087 A012194 this_sequence A041171 A111799 A135237
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KEYWORD
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sign,fini,full
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AUTHOR
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Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 12 2007
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