## An asymptotic for the growth of Markoff-Hurwitz tuples

Ryan Ronan

Baruch College, The City University of New York

December 8, 2017

For integer parameters $n \geq 3$, $a \geq 1$, and $k \geq 0$ the Markoff-Hurwitz equation is the diophantine equation

\[ x_1^2 + x_2^2 + \cdots + x_n^2 = ax_1x_2 \cdots x_n + k.\]