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On a conjecture of Carlitz. (English) Zbl 0635.12011
A conjecture of Carlitz on permutation polynomials is as follows: Given an even positive integer \(n\), there is a constant \(C_n\) such that if \(\mathbb F_q\) is a finite field of odd order \(q\) with \(q>C_n\) then there are no permutation polynomials of degree \(n\) over \(\mathbb F_q\). In this paper the author proves that the Carlitz conjecture is true if \(n=12\) or \(n=14\) and gives an equivalent version of the conjecture in terms of exceptional polynomials.

MSC:
11T06 Polynomials over finite fields
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