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A047694 x such that y^2 = C(x,0) + C(x,1) + C(x,2) + C(x,3) is soluble. 3

%I #24 Apr 30 2019 05:02:14

%S -1,0,2,7,15,74,767

%N x such that y^2 = C(x,0) + C(x,1) + C(x,2) + C(x,3) is soluble.

%C n such that A000125(n) is a perfect square. - _Frank M Jackson_, Mar 13 2013

%D R. K. Guy, Unsolved Problems in Number Theory, Section D3.

%H Andrew Bremner, <a href="https://doi.org/10.1090/S0025-5718-1975-0374019-7">An equation of Mordell,</a> Math. Comp., 29 (1975), pp. 925-928.

%H W. Ljunggren, <a href="https://doi.org/10.1112/jlms/s2-3.3.385">A diophantine problem</a>, J. London Math. Soc. (2), 3 (1971), pp. 385-391.

%F x such that 6y^2 = (x + 1)(x^2 - x + 6) has solutions in integers.

%t Select[Range[-10, 10^3], IntegerQ[Sqrt[((# + 1)(#^2 - # + 6))/6]] &] (* _Alonso del Arte_, Sep 13 2011 *)

%Y Cf. A047695.

%K sign,fini,full,nice

%O 0,3

%A _N. J. A. Sloane_

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Last modified March 28 04:58 EDT 2024. Contains 371235 sequences. (Running on oeis4.)