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. 39.

J. O. Button, The Uniqueness of the Prime Markoff Numbers,
J. London Math. Soc. (2) 58 (1998) pp. 917.

J. O. Button, Markoff Numbers, Principal Ideals and
Continued Fraction Expansions
J. Number Theory. (1) 87 (2001) pp. 7795.

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. 178183.
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. 187189, SpringerVerlag (Copernicus), New York, 1996.
ISBN 038797993X.

F. G. Frobenius, Über die Markoffschen Zahlen,
Sitzungsberichte der Königlich Preußischen Akadamie der
Wissenschaften zu Berlin, (1913), pp. 458487.
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,
SpringerVerlag, Berlin, 1968.

A. A. Markoff, Sur les formes binaires indéfinies,
Math. Ann. 17 (1880), pp. 379399.

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 2909467058.

G. Rosenberger, The Uniqueness of the Markoff Numbers, Mathematics
of Computation, Volume 30, Number 134, April 1976, pp. 361365.
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.
Markoff numbers on the web:

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).



Tom Ace
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