On Dudeney’s Round Table Problem for $p+2$

Abstract

Dudeney’s round table problem was proposed about one hundred years ago. It is already solved when the number of people is even, but it is still unsettled except for only a few cases when the number of people is odd.

In this paper, a solution of Dudeney’s round table problem is given when $n=p+2$, where $p$ is an odd prime number such that $2$ is the square of a primitive root of $\mathrm{G}\mathrm{F}(p)$, and $p\equiv 3(\mathrm{mod}4)$.