More numerical evidence on the uniqueness of Markov Numbers Academic Article uri icon


  • A Markov triple is a solution in postive integers of the equation x2+y2+z2=3 xyz. The maximum of the triple is a Markov Number. It is conjectured (Cassels "Introduction to Diophantine Approximations") that 2 distinct Markov triples cannot share the same Markov Number. Rosen & Patterson (Math. of Comp. 25 (1971)) tested the conjecture up to 1030 by direct computation of the Markov Numbers. Modular Arithmetic was used here to carry the computation up to 10105. No duplication was found. In addition the number of Markov numbers with N or less decimal digits is found to be approximately N2 as in Rosen & Patterson. 1975 BIT Foundations.

published proceedings

  • BIT Numerical Mathematics

author list (cited authors)

  • Borosh, I.

citation count

  • 1

complete list of authors

  • Borosh, I

publication date

  • January 1975