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The document defines Markoff numbers as positive solutions (x,y,z) to the Diophantine equation x^2 + y^2 + z^2 = 3xyz where x ≤ y ≤ z. This Markoff equation forms a tree with root (1,1,1) and branches generated by the operations (x,y,z) → (x,y,3xy-z), (x,y,z) → (x,z,3xz-y), and (x,y,z) → (y,z,3yz-x). The numbers z in ordered Markoff triples (x ≤ y ≤ z) are called Markoff numbers.

Author

Nicolas Ohina

Language

EN