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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

2 votes

Excellent uses of induction and recursion

There are infinifely many positive integers $n$ such that $2^n+1$ is divisible by $n$. One can show this by proving that if $n$ divides $2^n+1$, then $2^n+1$ divides $2^{2^n+1}+1$.
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