$latex M$ is the markov triple $(x,y,z)$: $x^2+y^2+z^2=xyz$ and $latex (x,y,x)\in \mathbb Z^3 \ \ \ \ (*)$. It is easy to see: $latex R_1: (x,y,z)\to (3yz-x,y,z)$. map markov triple to markov triple. This is also true for $latex R_2,R_3$. and the transform $latex R_1,R_2,R_3$ and permutation a classical result of Markov claim that all solutions of (*) could be generated from $latex (1,1,1)$. I got a similar result for a similar algebraic equation 1 half years ago when considering a …
