Fibonacci Numbers which equal the Square of their Index

Theorem
The only Fibonacci numbers which equal the square of their index are:

Proof
By definition of the Fibonacci numbers:

Then it is observed that $F_{12} = 144$.

After that, for $n > 12$, we have that $F_n > n^2$.

Also see

 * Square Fibonacci Number: after $144$, there are no more square Fibonacci numbers at all.