Computation in Markoff-Hurwitz Equations II

摘要

In the more than 100 years since Markoff-Hurwitz Equations, they play a decisive role, have turned up in an astounding variety of different settings, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words, from discrete mathematics to scientific computation. This paper is the continuation of our previous paper under the same title , which we refer to as Part I. In Part I: we introduced other people's work in this area, presented general properties of solutions, proved solution does not exist when n=3 and k=2, integer sequences and solutions were reported for n ≤10 and conjectures were posted. In this paper we prove that solution does not exist when (n=4, k=2), (n=4, k=3), (n=5, k=2) or (n=5, k=3).