Geodesic
The equivalent problem of testing Fermat primes
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 13-14.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the problem of testing Fermat numbers for primality is equivalent to the problem of testing some polynomials over $\mathrm{GF}(2)$ or $\mathrm{GF}(3)$ for irreducibility.
Keywords: irreducible polynomial, prime numbers, Fermat numbers. 
@article{PDMA_2014_7_a3,
     author = {Kr. L. Geut and S. S. Titov},
     title = {The equivalent problem of testing {Fermat} primes},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {13--14},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2014_7_a3/}
}
TY  - JOUR
AU  - Kr. L. Geut
AU  - S. S. Titov
TI  - The equivalent problem of testing Fermat primes
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2014
SP  - 13
EP  - 14
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2014_7_a3/
LA  - ru
ID  - PDMA_2014_7_a3
ER  - 
%0 Journal Article
%A Kr. L. Geut
%A S. S. Titov
%T The equivalent problem of testing Fermat primes
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2014
%P 13-14
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2014_7_a3/
%G ru
%F PDMA_2014_7_a3
Kr. L. Geut; S. S. Titov. The equivalent problem of testing Fermat primes. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 13-14. http://geodesic.mathdoc.fr/item/PDMA_2014_7_a3/

[1] Bolotov A. A., Gashkov S. B., Frolov A. B., Elementarnoe vvedenie v ellipticheskuyu kriptografiyu: algebraicheskie i algoritmicheskie osnovy, KomKniga, M., 2006

[2] Glusko Kr. L., Titov S. S., “O kvadratichnykh rasshireniyakh binarnykh polei”, Izvestiya Rossiiskogo gosudarstvennogo pedagogicheskogo universiteta im. A. I. Gertsena, 2013, no. 154, 7–16

[3] Geut Kr. L., Titov S. S., “O polikvadratichnom rasshirenii binarnykh polei”, Prikladnaya diskretnaya matematika. Prilozhenie, 2013, no. 6, 12–13

[4] Geut Kr. L., Titov S. S., “O generatsii neprivodimykh mnogochlenov prostykh poryadkov pri postroenii diskretnykh ustroistv SZhATiS”, Transport Urala, 2014, no. 1(40), 61–64

[5] Lidl R., Niderraiter G., Konechnye polya, Mir, M., 1988, 430 pp. | MR | Zbl

[6] Geut K. L., Titov S. S., “O generatsii i primenenii neprivodimykh mnogochlenov”, III Informatsionnaya shkola molodogo uchenogo, Cb. nauchnykh trudov, Ekaterinburg, 2013, 293–298

[7] Vinogradov I. M., Osnovy teorii chisel, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.–Izhevsk, 2003, 176 pp.