@angeliccanary Hi there! Thanks for these ideas. 🙂 It's really cool when you can find more than one, or even several, ways of doing the same problem. 🎆 🎆 🌠 You can definitely use the recursion definition of the Fibonacci sequence (which is very similar to what Prof. Loh did). I do think Prof. Loh was trying to find a different way to prove this pattern, rather than assuming the pattern was true, so I'm not sure about this:
or use the fact that we are finding GCD's of consecutive fibonacci numbers.
Great job 🙂 👍