Markoff-Rosenberger triples and generalized Lucas sequences

Hayder Hashim, László Szalay, Szabolcs Tengely

We consider the Markoff-Rosenberger equation $$a{x}^2+b{y}^2+c{z}^2=dxyz$$ with $(x,y,z)=(U_i,U_j,U_k),$ where $U_i$ denotes the $i$-th generalized Lucas number of first/second kind. We…