A Theorem on Permutations in a Finite Field

L. Carlitz
1960 Proceedings of the American Mathematical Society  
Let Fq denote the finite field of order q, where q = pn is odd. Put ip(a) = +1, -1 or 0 according as a is a nonzero square, a non-square or 0 in Fa. Then we have
doi:10.2307/2034798 fatcat:fkcczhyel5e27med23opi6dgj4