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I'm struggling to prove the following equation: $$ F_{n-1}F_{n-2}-F_nF_{n-3}=(-1)^n $$ You can verify this fact with this python code.

I managed to simplify the equation a little, so that only $F_{n-2}$ and $F_{n-3}$ left: $$ (F_{n-2})^2-F_{n-2}F_{n-3}-(F_{n-3})^2=(-1)^n $$ But I still don't see how to prove that.

Thanks in advance!

g00dds
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  • Hmm, how does the bot have permission to close based off of my single close vote? I would have thought at least two votes would be needed, to double-check – FShrike May 20 '23 at 17:57
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    @FShrike: “Community” here means that the author of the question confirmed it as a duplicate. – Martin R May 20 '23 at 17:58
  • To the op: Before you look at the linked post, I recommend you attempt some induction first. If you get stuck with the induction, you can find the answer in the linked post (and probably many other places on the internet) – FShrike May 20 '23 at 17:58
  • @MartinR Ah, thanks for clarifying – FShrike May 20 '23 at 17:58
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    See https://en.wikipedia.org/wiki/Cassini_and_Catalan_identities – Robert Z May 20 '23 at 18:55

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