Geodesic
On elements of high order in general finite fields
Algebra and discrete mathematics, Tome 18 (2014) no. 2, pp. 295-300.

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We show that the Gao's construction gives for any finite field $F_{q^{n}}$ elements with the multiplicative order at least $\binom{n+t-1}{t}\prod _{i=0}^{t-1}\frac{1}{d^{i}}$, where $d=\left\lceil 2\log _{q} n\right\rceil$, $t=\left\lfloor \log _{d} n\right\rfloor$.
Keywords: finite field, Diophantine inequality.
Mots-clés : multiplicative order 
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Roman Popovych. On elements of high order in general finite fields. Algebra and discrete mathematics, Tome 18 (2014) no. 2, pp. 295-300. http://geodesic.mathdoc.fr/item/ADM_2014_18_2_a9/

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