Filmor Theorem for integers

Alberto Borobia

Fillmore Theorem says that if $A$ is a nonscalar matrix of order $n$ over a field $\mathbb{F}$ and ${\gamma }_1,\dots ,{\gamma }_n\in \mathbb{F}$ are such that ${\gamma }_1+\cdots +{\gamma }_n=\text{tr}A$, the…