A227077 y solutions to the Diophantine equation 2*x^2*(x^2 - 1) = 3*(y^2 - 1).

1, 3, 7, 29, 6761

Offset: 0

Author

Raphie Frank, Jun 30 2013

Keywords

• nonn

Comments

Also solutions to (2*x^2 - 1)^2 = 6*y^2 - 5 as outlined in A180445, which gives the x solutions to this equation {1, 2, 3, 6, 91}.

(sqrt(2)*sqrt(sqrt(6*a(n)^2 - 5) + 1) - 1)^2 = A038198(n)^2 gives the Ramanujan-Nagell squares listed in A227078.

Links

• Richard K. Guy, The Strong Law of Small Numbers (example #29).

Crossrefs

Cf. A180445, A038198, A227078.

Programs

Mathematica

Select[Table[Sqrt[3-2x^2+2x^4]/Sqrt[3],{x,0,100}],IntegerQ]//Union (* Harvey P. Dale, Aug 11 2019 *)