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One problem that I found quite interesting is the Hadwiger-Nelson problem for coloring the plane. The proofs that the answer is at most $7$ and at least $4$ are easy and elegant (but also quite ...

A somewhat common belief among students starting out in cryptography:
Breaking RSA requires factoring the modulus.
Although it is not quite known to be a "false" belief, there is no known ...

Thanks to Ofer Zeitouni, unless I made some serious mistakes somewhere in the calculations, I've been able to find the exact answer using large deviations theory. The derivation of the final result is ...

$\newcommand{\expn}{\mathbb{E}}
\newcommand{\varn}{\operatorname{Var}}$
Following up on Brendan McKay's approach in the comments, let $v, w$ be two uniformly random vectors on the sphere. We are ...

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