A conjecture of Zhi-Wei Sun on determinants over finite fields [article]

Hai-Liang Wu, Yue-Feng She, He-Xia Ni
<span title="2022-01-13">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we study certain determinants over finite fields. Let 𝔽_q be the finite field of q elements and let a_1,a_2,⋯,a_q-1 be all nonzero elements of 𝔽_q. Let T_q=[1/a_i^2-a_ia_j+a_j^2]_1≤ i,j≤ q-1 be a matrix over 𝔽_q. We obtain the explicit value of T_q. Also, as a consequence of our result, we confirm a conjecture posed by Zhi-Wei Sun.
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