Markov number

A Markov number or Markoff number is a positive integer x, y or z that is part of a solution to the Markov Diophantine equation

${\displaystyle x^{2}+y^{2}+z^{2}=3xyz,\,}$

studied by Andrey Markoff (1879, 1880).

The first few Markov numbers are

1, 2, 5, 13, 29, 34, 89, 169, 194, 233, 433, 610, 985, 1325, ... (sequence A002559 in the OEIS)

appearing as coordinates of the Markov triples

(1, 1, 1), (1, 1, 2), (1, 2, 5), (1, 5, 13), (2, 5, 29), (1, 13, 34), (1, 34, 89), (2, 29, 169), (5, 13, 194), (1, 89, 233), (5, 29, 433), (1, 233, 610), (2, 169, 985), (13, 34, 1325), ...

There are infinitely many Markov numbers and Markov triples.