Markoff numbers (references)

Selected books and articles regarding the Markoff numbers:

• A. Baragar, On the Unicity Conjecture for Markoff Numbers, Canad. Math. Bull. Vol. 39 (1), 1996 pp. 3-9.
• J. O. Button, The Uniqueness of the Prime Markoff Numbers, J. London Math. Soc. (2) 58 (1998) pp. 9-17.
• J. O. Button, Markoff Numbers, Principal Ideals and Continued Fraction Expansions J. Number Theory. (1) 87 (2001) pp. 77-95.
• J. W. S. Cassels, An Introduction to Diophantine Approximation, Chapter II, Cambridge University Press, Cambridge, 1957.
• H. Cohn, Growth Types of Fibonacci and Markoff, Fibonacci Quarterly (2) v.17 (1979), pp. 178-183. This interesting paper includes a method of calculating Markoff numbers using matrix multiplication that differs from the method I have described.
• J. H. Conway and R. K. Guy, The Book of Numbers, pp. 187-189, Springer-Verlag (Copernicus), New York, 1996. ISBN 0-387-97993-X.
• F. G. Frobenius, Über die Markoffschen Zahlen, Sitzungsberichte der Königlich Preußischen Akadamie der Wissenschaften zu Berlin, (1913), pp. 458-487. This is an extensive and interesting paper. The original journal may be hard to locate; a copy of the paper appears as chapter 96 in Band III of Ferdinand Georg Frobenius  Gesammelte Abhandlungen, Springer-Verlag, Berlin, 1968.
• A. A. Markoff, Sur les formes binaires indéfinies, Math. Ann. 17 (1880), pp. 379-399.
• S. Perrine, matricielle de la théorie de Markoff classique, International Journal of Mathematics and Mathematical Sciences, 32:4, October 2002.
• S. Perrine, La théorie de Markoff et ses développements, Tessier & Ashpool, Chantilly, 2002. ISBN 2-9094-6705-8.
• G. Rosenberger, The Uniqueness of the Markoff Numbers, Mathematics of Computation, Volume 30, Number 134, April 1976, pp. 361-365. This paper claimed to prove the unicity conjecture, but was flawed as pointed out by R. Bumby in MR 53 (1977) 280.
• V. Senkel, Markoffzahlen. http://www.minortriad.com/senkel.pdf   This dissertation (PDF, German language) concisely and clearly presents a number of points about the Markoff numbers.

• N. J. A. Sloane, Sequence A002559 in The On-Line Encyclopedia of Integer Sequences. http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A002559
• Eric W. Weisstein and Wolfram Research, Inc., Markov Number. http://mathworld.wolfram.com/MarkovNumber.html
• Qing Zhou, On the uniqueness conjecture for Markoff triples. http://arxiv.org/abs/math.GT/0010131v1   Yet another paper claiming to prove the unicity conjecture, "withdrawn by author due to an error in the proof" (see http://arxiv.org/abs/math.GT/0010131 ).

Should Markoff be spelled -off or -ov? "Markoff" is more often used when discussing his work in number theory (e.g., Markoff numbers); "Markov" tends to be used when discussing his work in probability (e.g. Markov chains).