Geodesic
17 necessary and sufficient conditions for the primality of Fermat numbers
Communications in Mathematics, Tome 11 (2003) no. 1, pp. 73-79 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 05C20, 11A07, 11A51 
@article{COMIM_2003_11_1_a4,
     author = {K\v{r}{\'\i}\v{z}ek, Michal and Somer, Lawrence},
     title = {17 necessary and sufficient conditions for the primality of {Fermat} numbers},
     journal = {Communications in Mathematics},
     pages = {73--79},
     year = {2003},
     volume = {11},
     number = {1},
     mrnumber = {2037310},
     zbl = {1227.11029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2003_11_1_a4/}
}
TY  - JOUR
AU  - Křížek, Michal
AU  - Somer, Lawrence
TI  - 17 necessary and sufficient conditions for the primality of Fermat numbers
JO  - Communications in Mathematics
PY  - 2003
SP  - 73
EP  - 79
VL  - 11
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/COMIM_2003_11_1_a4/
LA  - en
ID  - COMIM_2003_11_1_a4
ER  - 
%0 Journal Article
%A Křížek, Michal
%A Somer, Lawrence
%T 17 necessary and sufficient conditions for the primality of Fermat numbers
%J Communications in Mathematics
%D 2003
%P 73-79
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/COMIM_2003_11_1_a4/
%G en
%F COMIM_2003_11_1_a4
Křížek, Michal; Somer, Lawrence. 17 necessary and sufficient conditions for the primality of Fermat numbers. Communications in Mathematics, Tome 11 (2003) no. 1, pp. 73-79. http://geodesic.mathdoc.fr/item/COMIM_2003_11_1_a4/

[1] Btermann K.-R.: Thomas Clausen, Mathematiker und Astronom. J. Reine Angew. Math. 216, 1964, 159-198. | MR

[2] Crandall R. E., Mayer E., Papadopoulos J.: The twenty-fourth Fermat number is composite. Math. Comp., accepted, 1999, 1-21.

[3] Gauss C. P.: Disquisitiones arithmeticae. Springer, Berlin 1986. | MR | Zbl

[4] Inkeri K.: Tests for primality. Ann. Acad. Sci. Fenn. Ser. A I No. 279 1960, 1-19. | MR | Zbl

[5] Jones R,, Pearce J.: A postmodern view of fractions and the reciprocals of Fermat primes. Math. Mag. 73, 2000, 83-97. | DOI | MR

[6] Křížek M., Chleboun J.: A note on factorization of the Fermat numbers and their factors of the form $3h2^n + 1$. Math. Bohem. 119, 1994, 437-445. | MR

[7] Křížek M., Luca F., Somer L.: 17 lectures on the Fermat numbers. From number theory to geometry. Springer-Verlag, New York 2001. | MR

[8] Křížek M., Somer L.: A necessary and sufficient condition for the primality of Fermat numbers. Math. Bohem. 126, 2001, 541-549. | MR

[9] Luca F.: Fermat numbers and Heron triangles with prime power sides. Amer. Math. Monthly, accepted in 2000.

[10] Lucas E.: Theoremes d'arithmétique. Atti della Reale Accademia delle Scienze di Torino 13, 1878, 271-284.

[11] Mcintosh R.: A necessary and sufficient condition for the primality of Fermat numbers. Amer. Math. Monthly 90, 1983, 98-99. | DOI | MR | Zbl

[12] Morehead J. C.: Note on Fermat's numbers. Bull. Amer. Math. Soc. 11, 1905, 543-545. | DOI | MR

[13] Pepin P.: Sur la formule $2^{2^n} + 1$. C. R. Acad. Sci. 85, 1877, 329-331.

[14] Somer L., Křížek M.: On a connection of number theory with graph theory. Czechoslovak Math. J. (submitted) | MR

[15] Szalay L.: A discrete iteration in number theory. (Hungarian), BDTF Tud, Kozi. VIII. Termeszettudomanyok 3., Szombathely, 1992, 71-91. | Zbl

[16] Vasilenko O. N.: On some properties of Fermat numbers. (Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh., no. 5 1998, 56-58. | MR | Zbl

[17] Wantzel P. L.: Recherches sur les moyens de reconnaitre si un Probleme de Geometrie peut se resoudre avec la regie et le compas. J. Math. 2, 1837, 366-372.