Abstract
A geometric approach is introduced to study permutation polynomials over a finite field. As an application, we prove that there are no permutation polynomials of degree 2 l 2l over a large finite field, where l l is an odd prime. This proves that the Carlitz conjecture is true for n = 2 l n = 2l . Previously, the conjecture was known to be true only for n ≤ 16 n \leq 16 .
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