  In this paper we study some determinants and permanents. In particular, we
investigate the new-type determinants $$\det[(i^2+cij+dj^2)^{p-2}]_{1\le i,j\le
p-1}\ \text{and} \ \det[(i^2+cij+dj^2)^{p-2}]_{0\le i,j\le p-1}$$ modulo an odd
prime $p$, where $c$ and $d$ are integers. We also pose some conjectures for
further research.

Number Theory