Summary: For an integer \(d\ge 2\) which is not a square, we show that there is at most one positive integer \(x\) appearing in a solution of the Pell equation \(x^2-dy^2=\pm 4\) which is a Fibonacci number, except when \(d=2, 5\), where we have exactly two values of \(x\) being members of the Fibonacci sequence.
Part I see [Math. Scand. 122, No. 1, 18–30 (2018;
Zbl 1416.11027)].
