Suppose the positive integers satisfy
is a Triangular number [ ]
numbers of the form are Second pentagonal numbers.
Equation (1) gives us the Pell equation:
The first few solutions are:
(x, y) = (0,0), (22,18), (2180,1780), (213642,174438), (20934760,17093160), (2051392862,1674955258)
Show that for all that satisfy
are all perfect squares.