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arXiv · 2207.13039

On some determinants and permanents

Zhi-Wei Sun
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Abstract

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.

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Zhi-Wei Sun. 2022-07-26. On some determinants and permanents. https://arxiv.org/abs/2207.13039

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