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Congratulations to one of the most brilliant young minds in the Brilliant community for passing the PMO Area Stage Qualifiers - @Sean Anderson Ty. I say that this is a great feat for there are many who had the chance but wasn't able to qualify (Yep, I'm talking about me) He also lives/studies in the same city as I am, so I am proud that maybe one of ours is going to be part of IMO.  As a gift, I give these Fibonacci problems (Who doesn't like proving?) 1) Let $$m$$ and $$n$$ be positive integers. Prove that, if $$m$$ is divisible by $$n$$, then, $$f_{m}$$ is divisible by $$f_{n}$$.  2) Let $$m$$ and $$n$$ be positive integers whose greatest common divisor is $$d$$. Prove that the greatest common divisor of the Fibonacci numbers $$f_{m}$$ and $$f_{n}$$ is the Fibonacci number $$f_{d}$$

Note by Marc Vince Casimiro
1 year, 10 months ago

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@Sean Ty · 1 year, 10 months ago