A Mean Value Property in Powers of the Natural Square

Paul Jolissaint, Kenichi Takemura

Let $n\ge 1$ be an odd integer, set $m=(n-1)/2$ and let $M$ be an $n\times n$ matrix whose coefficients are of the form $M_{i,j}=aij+bi+cj+d$ where $0\le i,j\le n-1$. Then we pr…