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

1, 49, 289, 5041, 274266721

Offset: 0

Author

Raphie Frank, Aug 08 2013

Keywords

• nonn
• fini
• full

Comments

x = {1, 2, 3, 6, 91} = A180445(n).

y = {1, 3, 7, 29, 6761} = A227077(n).

(sqrt(2*sqrt(n) + 2) - 1)^2 is a Ramanujan-Nagell Square = {1, 9, 25, 121, 32761} = A227078(n).

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 181, p. 56, Ellipses, Paris 2008.
• L. J. Mordell, Diophantine Equations, Academic Press, NY, 1969, p. 205.

Links

• Richard K. Guy, The Strong Law of Small Numbers (example #29).
• Eric Weisstein's World of Mathematics, Ramanujan's Square Equation

Crossrefs

Cf. A060728, A180445, A227077, A227078.