On the structure of solutions graph of the Markoff-Hurwitz equation and recurrence sequences

2025/09/23 by Vyugin, Ilya V.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.19289

Abstract

We prove that almost all solutions of the Markoff-Hurwitz equation over a residue field modulo p can be obtained from one another by a chain of natural transformations. We also study recurrence sequences considered modulo prime p.

Citations

• Nonabelian level structures, Nielsen equivalence, and Markoff triples
• Markoff Triples and Strong Approximation

Related

• Fundamental domain for the Markoff-Hurwitz equation
• Nonabelian level structures, Nielsen equivalence, and Markoff triples
• An asymptotic formula for integer points on Markoff-Hurwitz varieties
• Estimates on the number of rational solutions of Markoff-Hurwitz equations over finite fields
• Connectedness of special points in the Markoff mod p graphs