Legendre symbols related to certain determinants

Xin-Qi Luo, Zhi-Wei Sun

Let $p$ be an odd prime. For $b,c\in \mathbb{Z}$, Sun introduced the determinant $$D_p(b,c)={\left|(i^2+bij+c{j}^2{)}^{p-2}\right|}_{1⩽i,j⩽p-1},$$ and investigated the L…