Square Fibonacci Number

Theorem

After $1$, there exists exactly one Fibonacci number which is also square:

$F_{12} = 144 = 12^2$

which is also coincidentally the square of its index.

Proof

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Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $144$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $144$