Geodesic
Some problem of finite fields
Čebyševskij sbornik, Tome 12 (2011) no. 3, pp. 64-76

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The paper shows an example of $F_{9}$, that if in the extended field to take two different primitive elements $\alpha$ and $\beta$ and two distinct primitive polynomials in this field of the same degree, so that the coefficients of these polynomials are represented as powers of primitive elements respectively, the equality of the exponents of powers before similar powers of x is performed under the isomorphism of Frobenius. 
@article{CHEB_2011_12_3_a6,
     author = {O. Cuellar Justiz},
     title = {Some problem of finite fields},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {64--76},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2011_12_3_a6/}
}
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O. Cuellar Justiz. Some problem of finite fields. Čebyševskij sbornik, Tome 12 (2011) no. 3, pp. 64-76. http://geodesic.mathdoc.fr/item/CHEB_2011_12_3_a6/