On a real analysis worksheet i was given, the following question is posited.

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> Let $f\_n$ be the Fibonacci sequence defined by $f\_1=1, f\_2=1$ and for $n>2, f\_{n+1}=f\_n+f\_{n-1}$. Show that for all $n>2,$ $$f\_{n+1}f\_{n-1}=(-1)^nf\_n^2$$
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I can't help but think that this is a typo. All Fibonacci numbers are positive, and a basic substitution of $n=3$ would give

$$f\_{4}f\_2=3\neq-4=(-1)^3f\_3^2$$

If it is a typo, does anyone know the actual identity that is being questioned here?