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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
##### Keywords:
permutation polynomials; finite field