More numerical evidence on the uniqueness of Markov Numbers Academic Article

abstract

• 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.

authors

• Borosh, Itshak

published proceedings

• BIT Numerical Mathematics

author list (cited authors)

• Borosh, I.

citation count

• 1

complete list of authors

• Borosh, I

publication date

• January 1975

publisher

• Springer Nature  Publisher

published in

• BIT Numerical Mathematics  Journal

Digital Object Identifier (DOI)

• 10.1007/bf01931671

start page

• 351

end page

• 357

volume

• 15

issue

• 4

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fbf01931671