On the X-coordinates of Pell equations which are products of two Fibonacci numbers.

For an integer d ≥ 2 which is not a square, we show that there is at most one value of the positive integer X participating in the Pell equation X 2 − d Y 2 = ± 1 which is a product of two Fibonacci numbers, with a few exceptions that we completely characterize. [ABSTRACT FROM AUTHOR]