Quadratic forms representing the $p$-th Fibonacci number

Pedro Berrizbeitia, Florian Luca, Alberto Mendoza

In this paper, we show that if $p\equiv 1(\mathrm{mod}4)$ is prime, then $4F_p$ admits a representation of the form $u^2-p{v}^2$ for some integers $u$ and $v$, where $F_n$ is the $n$th Fibon…