On R. Chapman's ``evil determinant'': case p≡1±od4

Abstract

For $p\equiv 1\ ({\rm mod}\,4)$, we prove the formula (conjectured by R. Chapman) for the determinant of the $\frac {p+1}{2}\times \frac {p+1}{2}$ matrix $C=(C_{ij})$ with $C_{ij}=\genfrac {(}{)}{}{1}{j-i}{p}$.