Michael E. Zieve:
Some families of permutation polynomials over finite fields,
Int. J. Number Theory 4 (2008), 851–857.

(Both the published version and the arXiv version are available online.)

We give necessary and sufficient conditions for a polynomial of the form  xr(1+xv+x2v+...+xkv)t  to permute the elements of the finite field  Fq.  Our results yield especially simple criteria in case  (q-1) / gcd(q-1, v) is a small prime. In case this prime is at most 7 and the polynomial is a binomial, this yields the results of L. Wang and A. Akbary–Q. Wang, which were proved by more complicated methods.


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