MathOverflow

Suppose we have natural numbers $n_1< n_2< \cdots <n_k$ such that $1=1/n_1+\cdots+1/n_k$. What can we say about such natural numbers? If I would have known that there aren't such $n_i$'s, then that would have given a trivial answer to something...

Consider the following variant of the full-information secretary problem.
Let $M \in \mathbb{N}$, and suppose we observe a sequence of $M$ i.i.d.\ random variables$$X_1, X_2, \dots, X_M,$$each uniformly distributed on the discrete set $\{1,2,\dots,M\}$....

Question. Can the alternating group $\mathrm{Alt}(X)$ on a finite set $X$ of cardinality $|X|=n$ be generated by a sharply $2$-transitive set $\bigcup_{i=1}^{n-1}B_if_i$ such that for every $i<n$, $B_i$ is a Boolean sharply transitive subgroup of...

Let$$H_n:=\sum_{0<k\le n}\frac1k\ \ \ \ (n=0,1,2,\ldots).$$Inspired by Question 507603 and Question 507592, I discovered the following identity$$\sum_{k=0}^\infty\frac{\binom{2k}k^2\binom{3k}k}{(-192)^k}\left(3H_{3k}+2H_{2k}-5H_{k}\right)=\frac{...