Fibonacci numbers are defined as $f_0 = f_1 = 1$ and $f_{n+1} = f_n + f_{n-1}$.
Show that a number $F$ is a fibonacci number if and only if one of $5F^2 \pm 4$ is a perfect square.
Show that a number $F$ is a fibonacci number if and only if one of $5F^2 \pm 4$ is a perfect square.
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