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%I #15 Sep 08 2022 08:45:31
%S -1,0,3,4,75
%N Integers n such that n^3 - (n + 2)^2 + n + 4 is a square.
%C 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
%e 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.
%o (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 */
%o (SageMath) [i[0] for i in EllipticCurve([0, -1, 0, -3, 0]).integral_points()] # _Seiichi Manyama_, Aug 26 2019
%Y Cf. A005563, A028560.
%K sign,fini,full
%O 1,3
%A _Mohamed Bouhamida_, Nov 12 2007
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