Permutation properties of the polynomials 1+𝑥+\cdots+𝑥^{𝑘} over a finite field

Matthews, Rex

doi:10.1090/S0002-9939-1994-1165062-2

Permutation properties of the polynomials $1+x+\cdots+x\sp k$ over a finite field

Author: Rex Matthews
Journal: Proc. Amer. Math. Soc. 120 (1994), 47-51
MSC: Primary 11T06
DOI: https://doi.org/10.1090/S0002-9939-1994-1165062-2
MathSciNet review: 1165062
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Abstract: It is shown that a polynomial of the shape $1 + x + \cdots + {x^k}$ is a permutation polynomial over a finite field ${\mathbb{F}_q}$ of odd characteristic if and only if $k \equiv 1\bmod p(q - 1)$ .

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