Some Studies on Markov-Type Equations

  • Zhi-Xiong Wen
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


A concept of prime solution is introduced in solving Markoff-type equations and the structure of solutions is discussed.


Fundamental Solution Symmetric Group Integer Solution Diophantine Equation Minimum Property 
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  1. 1.
    A. Baragar, Products of consecutive integers and the Markoff equation, Aequationes Math. 51 (1996), 129–136.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    J. W. S. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press, Cambridge, UK (1957).MATHGoogle Scholar
  3. 3.
    A. N. W. Hone, Diophantine non-integrability of a third-order recurrence with the Laurent property, J. Phys. A: Math. Gen. 39 (2006), L171–L177. A.
  4. 4.
    A. Hurwitz, Über eine Aufgabe der unbestimmten Analysis, Archiv Math. Phys. 3 (1907) 185–196; and Mathematische Werke, Vol. 2, Chap. LXX (1933 and 1962) 410–421.Google Scholar
  5. 5.
    A. A. Markoff, Sur les formes quadratiques binaires indéfinies, Math. Ann., 15 (1879), 381–406. Google Scholar
  6. 6.
    L. J. Mordell. On the integer solutions of the equation x 2+y 2+z 2+2xyz=n, J. Lond. Math. Soc., 28 (1953), 500–510.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    H. Schwartz and H. T. Muhly, On a class of cubic Diophantine equations. J. Lond. Math. Soc., 32 (1957), 379–382.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsHuazhong University of Science and TechnologyWuhanP. R. China

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