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A133475 Integers n such that n^3 + n^2 - 9*n + 16 is a square. 0
-4, -3, -1, 0, 1, 3, 5, 11, 15, 28, 47, 55, 81, 549, 1799, 8361 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The set of x values of integral points on the elliptic curve y^2 = x^3 + x^2 - 9*x + 16.
LINKS
EXAMPLE
0^3 + (-5)^2 + (-9) = 4^2, 1^3 + (-4)^2 + (-8) = 3^2, 3^3 + (-2)^2 + (-6) = 5^2
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 ] (* Jean-François Alcover, Sep 07 2011 *)
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()
(PARI) is(n)=issquare(n^3+n^2-9*n+16) \\ Charles R Greathouse IV, Sep 06 2016
CROSSREFS
Sequence in context: A144161 A054669 A131027 * A242106 A294885 A021236
KEYWORD
sign,full,fini
AUTHOR
Mohamed Bouhamida, Nov 29 2007
EXTENSIONS
Edited by Max Alekseyev, Nov 13 2009
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)