login
A227079
Solutions n to the Diophantine equation: n = (2*x^2 - 1)^2 = (6*y^2 - 5).
0
1, 49, 289, 5041, 274266721
OFFSET
0,2
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
KEYWORD
nonn,fini,full
AUTHOR
Raphie Frank, Aug 08 2013
STATUS
approved