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I have seen this question posted somewhere on this site before, but they included a lemma in which $$_{2−1}=F^2_+F^2_{−1}$$ This wasn't demonstrated to me through my textbook, and I was asked to prove the same question. So I am curious if there is another way to prove this question without such a lemma. I tried relating the $F_{2n}$ term without this lemma but failed, so I want to know whether or not this is possible without that lemma.

I am very new to number theory, so in addition to this question, can I get some advice on how to improve in this field of mathematics and how should I spot which lemma or theorems are needed for a question?

Kevin Zhang
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  • Does [https://math.stackexchange.com/questions/267309/fibonacci-lucas-numbers-relationship-f-2n-f-n-l-n?rq=1](this MSE answer) help you out? – Eric Snyder Aug 17 '22 at 04:08
  • sorry, i was looking at a different article on MSE, haha well thanks so much man appreciate it – Kevin Zhang Aug 17 '22 at 04:18

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