2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123053We present a very elementary proof of the uniqueness of Markoff numbers which are prime powers or twice prime powers, in the sense that it uses neither algebraic number theory nor hyperbolic geometry.14 pages, 3 figures. Version 2: thoroughly rewritten, title changedNumber Theory11D45; 11J06; 20H10An elementary proof of uniqueness of Markoff numbers which are prime powerstext