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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Some numerical evidence concerning the uniqueness of the Markov numbers
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by D. Rosen and G. S. Patterson PDF
Math. Comp. 25 (1971), 919-921 Request permission


A Markov triple is a set of three positive integers satisfying the diophantine equation $({x^2} + {y^2} + {z^2} = 3xyz)$. 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 $(p,{a_1},{b_1})$ and $(p,{a_2},{b_2})$, 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.
  • J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR 0087708
  • L. E. Dickson, Studies in the Theory of Numbers, Univ. of Chicago Press, Chicago, Ill., 1930. G. Frobenius, “Über die Markoffschen Zahlen,” S.-B. Preuss. Akad. Wiss., v. 1913, pp. 458-487.
  • Donald E. Knuth, The art of computer programming, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. Volume 1: Fundamental algorithms. MR 0378456
  • A. Markoff, “Sur les formes quadratiques binaires indefinées,” Math. Ann., v. 15, 1879, pp. 381-409.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 919-921
  • MSC: Primary 10B10
  • DOI:
  • MathSciNet review: 0300972