I have wrestled with the following two problems for a couple of hours each and have been successful. Now I am interested in how a more experienced mathematician would go about solving these.(adsbygoogle = window.adsbygoogle || []).push({});

I encourage you to look past my lack of latex skills (lol), and do your best with the attachment I poorly put together.

A note about the second problem, If anyone is unaware F denotes the Fibonacci numbers and L denotes the Lucas numbers. Second, the term on the left side is a little blurry but it says the 2n Fibonacci number. Also I challenge you to solve this second problem without strong induction. Which I semi-managed to do. I proved a secondary result with strong induction then used that result to use regular induction on the main problem.

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# 2 number theory problems

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