James Propp <jamespropp@gmail.com> wrote:

How many Fibonacci numbers are of the form n^2-n-1?

For positive Fibonacci numbers less than 2^63, none except 1, 5, 55, and 89. If I replace one or both minus signs with plus signs, there are still no solutions above 89 (though there are a few more below it). Similarly if I leave out the n or the 1 (leaving n^2), except that 144 is of course square.