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Elements of provable high orders in finite fields

Author: Shuhong Gao
Journal: Proc. Amer. Math. Soc. 127 (1999), 1615-1623
MSC (1991): Primary 11T55; Secondary 11Y16, 68Q25, 11T06, 12Y05
Published electronically: February 11, 1999
MathSciNet review: 1487368
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Abstract: A method is given for constructing elements in ${\mathbb F}_{q^n}$ whose orders are larger than any polynomial in $n$ when $n$ becomes large. As a by-product a theorem on multiplicative independence of compositions of polynomials is proved.

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Additional Information

Shuhong Gao
Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-1907

Keywords: Finite fields, primitive elements, elements of provable high orders, compositions of polynomials
Received by editor(s): September 16, 1997
Published electronically: February 11, 1999
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society

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