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A227079 Solutions n to the Diophantine equation: n = (2*x^2 - 1)^2 = (6*y^2 - 5).

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%I A227079 #21 Feb 16 2025 08:33:20
%S A227079 1,49,289,5041,274266721
%N A227079 Solutions n to the Diophantine equation: n = (2*x^2 - 1)^2 = (6*y^2 - 5).
%C A227079 x = {1, 2, 3, 6, 91} = A180445(n).
%C A227079 y = {1, 3, 7, 29, 6761} = A227077(n).
%C A227079 (sqrt(2*sqrt(n) + 2) - 1)^2 is a Ramanujan-Nagell Square = {1, 9, 25, 121, 32761} = A227078(n).
%D A227079 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 181, p. 56, Ellipses, Paris 2008.
%D A227079 L. J. Mordell, Diophantine Equations, Academic Press, NY, 1969, p. 205.
%H A227079 Richard K. Guy, <a href="http://www.jstor.org/stable/2322249">The Strong Law of Small Numbers</a> (example #29).
%H A227079 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujansSquareEquation.html">Ramanujan's Square Equation</a>
%Y A227079 Cf. A060728, A180445, A227077, A227078.
%K A227079 nonn,fini,full
%O A227079 0,2
%A A227079 _Raphie Frank_, Aug 08 2013