Abstract
We shall establish for all finite fields GF( p n ) the following result of Chowla: given a positive integer m greater than one and the finite field GF( p), p a prime, such that x m = −1 is solvable in GF( p), then there exists an absolute positive constant c, c ≤ 10 ln 2 , such that for each set of s nonzero elements a i of GF( p), a 1x 1 m + ⋯ + a sx s m has a non-trivial zero in GF( p) if s ≥ c ln m.
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