Let $F_p = \{0,1,2,...,p-1\}$ be field for a prime $p$. Does there exist a matrix $A$ with entries in $F_p$ such that $tr(A^k) = 0$ if $k=2,3,\ldots,p-1$ and $tr(A^k) \neq 0$ if $k=1$?
2026-03-25 09:27:18.1774430838
Existence of matrix with certain property over a finite field
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