The Kauffman–Harary conjecture for prime-determinant alternating knot diagrams

Let $D$ be a reduced alternating diagram of a knot $K$ with determinant $p$, where $p$ is prime. A Fox $p$-coloring is a coloring of the arcs of $D$ by elements of $\mathbb Z_p$ satisfying the crossing relations, and it is non-trivial when not all arcs receive the same color. Kauffman–Harary conjecture. Every non-trivial $p$-coloring of $D$ assigns different colors to different arcs.

The conjecture was proved in full generality by Mattman and Solis using pseudo-colorings, so it is no longer open.