Abstract
In this paper, we study some arithmetic properties of certain Toeplitz-type matrices over finite fields. For example, suppose {α1,…,αn} are all the nonzero k-th powers in a finite field and for 1⩽i,j⩽n, we setxij={1αi−αjif i≠j,0if i=j. We give an explicit formula for the characteristic polynomial of [xij]1⩽i,j⩽n and confirm several conjectures posed by Zhi-Wei Sun.
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