  In this paper we first investigate minimal sufficient sets of colors for p=11
and 13. For odd prime p and any p-colorable link L with non-zero determinant,
we give alternative proofs of mincol_p L \geq 5 for p \geq 11 and mincol_p L
\geq 6 for p \geq 17. We elaborate on equivalence classes of sets of distinct
colors (on a given modulus) and prove that there are two such classes of five
colors modulo 11, and only one such class of five colors modulo 13. Finally, we
give a positive answer to a question raised by Nakamura, Nakanishi, and Satoh
concerning an inequality involving crossing numbers. We show it is an equality
only for the trefoil and for the figure-eight knots.

Geometric Topology