Geodesic
Nonexistence of permutation binomials of certain shapes
The electronic journal of combinatorics, Tome 14 (2007)

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Suppose $x^m+ax^n$ is a permutation polynomial over ${\Bbb F}_p$, where $p>5$ is prime and $m>n>0$ and $a\in{\Bbb F}_p^*$. We prove that $\gcd(m-n,p-1)\notin\{2,4\}$. In the special case that either $(p-1)/2$ or $(p-1)/4$ is prime, this was conjectured in a recent paper by Masuda, Panario and Wang.
DOI : 10.37236/1013
Classification : 11T06 
Ariane M. Masuda; Michael E. Zieve. Nonexistence of permutation binomials of certain shapes. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/1013
@article{10_37236_1013,
     author = {Ariane M. Masuda and Michael E. Zieve},
     title = {Nonexistence of permutation binomials of certain shapes},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/1013},
     zbl = {1162.11396},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1013/}
}
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