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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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 $ p$ if and only if $ k \equiv 1\bmod p(q - 1)$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1165062-2
PII: S 0002-9939(1994)1165062-2
Article copyright: © Copyright 1994 American Mathematical Society