Some Numerical Evidence Concerning the Uniqueness of the Markov Numbers
Mathematics of Computation1971Vol. 25(116), pp. 919–919
Abstract
A Markov triple is a set of three positive integers satisfying the diophantine equation (x* + y1 + z2 = 3xyz).The maximum of the triple is called a Markov number.Although all Markov triples can be generated from the triple (1,1,1), it is not known whether it is possible to obtain (p, ax, b) and (p, o2, >2), where p is the same Markov number for both triples.All Markov numbers not exceeding 30 digits were computed without turning up a duplication, lending some credence to the conjecture that the Markov numbers are unique.
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