Waring Problem for Matrices over Finite Fields

Krishna Kishore, Adrian Vasiu, Sailun Zhan

We prove that for all integers $k\ge 1$, $q\ge (k-1{)}^4+6k$, and $m\ge 1$, every matrix in $M_m({\mathbb{F}}_q)$ is a sum of two kth powers: $M_m(\mathbb F_q)=\{A^k+B^k|A,B\in M_…