Markov Number
The Markov numbers 
occur in solutions to the Diophantine Equation
and are related to Lagrange Numbers
by
The first few solutions are
, (1, 1, 2), (1, 2, 5), (1, 5, 13), (2, 5, 29), .... The solutions can bearranged in an infinite tree with two smaller branches on each trunk. It is not known if two different regions can have thesame label. Strangely, the regions adjacent to 1 have alternate Fibonacci Numbers 1, 2, 5, 13, 34,..., and the regions adjacent to 2 have alternate Pell Numbers 1, 5, 29, 169, 985, ....Let 
be the number of Triples with 
, then
where
(Guy 1994, p. 166).See also Hurwitz Equation, Hurwitz's Irrational Number Theorem, Lagrange Number (Rational Approximation)Liouville's Rational ApproximationTheorem, Liouville-Roth Constant, Roth's Theorem, Segre's Theorem,Thue-Siegel-Roth TheoremReferences
Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 187-189, 1996. Guy, R. K. ``Markoff Numbers.'' §D12 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 166-168, 1994.
- Legendre Quadrature
- Legendre Relation
- Legendre's Chi-Function
- Legendre's Constant
- Legendre Series
- Legendre's Factorization Method
- Legendre's Formula
- Legendre's Quadratic Reciprocity Law
- Legendre Sum
- Legendre Symbol
- Legendre Transformation
- Lehmer Method
- Lehmer Number
- Lehmer-Schur Method
- Lehmer's Constant
- Lehmer's Formula
- Lehmer's Phenomenon
- Lehmer's Problem
- Lehmer's Theorem
- Lehmus' Theorem
- Leibniz Criterion
- Leibniz Harmonic Triangle
- Leibniz Identity
- Leibniz Integral Rule
- Leibniz Series