Just the other night, before I went to bed, I was trying to work out the solution to a proof by induction involving a combination of Fibonacci numbers.
In my sleep, I worked though some math involving the Fibonacci numbers, taking the gcd(), multiplying sequences of them. I didn't solve the problem, but when I woke up, I had a better understanding of what I could try.
I find this happens a lot when I'm studying subjects like number theory. My best insights are when I'm asleep (or in the shower).
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