All Questions

Let $S=\{x_1,\ldots,x_k\}$ be a set of $k$ distinct natural numbers, a subset of $\{1,\ldots,n\} = \mathbb{N}_{\le n}$. Define the common-factor graph $G(S)$ as the (undirected) graph with a node for ...

This post was inspired by the Square-Sum Problem presented in Numberphile by Matt Parker. He asked about Hamiltonianness for $n=2$, and we ask about connectedness for all $n \in \mathbb{N}^*$. ...