| Title:
|
17 necessary and sufficient conditions for the primality of Fermat numbers (English) |
| Author:
|
Křížek, Michal |
| Author:
|
Somer, Lawrence |
| Language:
|
English |
| Journal:
|
Acta Mathematica et Informatica Universitatis Ostraviensis |
| ISSN:
|
1211-4774 |
| Volume:
|
11 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
73-79 |
| . |
| Category:
|
math |
| . |
| MSC:
|
05C20 |
| MSC:
|
11A07 |
| MSC:
|
11A51 |
| idZBL:
|
Zbl 1227.11029 |
| idMR:
|
MR2037310 |
| . |
| Date available:
|
2009-01-30T09:10:34Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120594 |
| . |
| Reference:
|
[1] Btermann K.-R.: Thomas Clausen, Mathematiker und Astronom.J. Reine Angew. Math. 216, 1964, 159-198. MR 0164862 |
| Reference:
|
[2] Crandall R. E., Mayer E., Papadopoulos J.: The twenty-fourth Fermat number is composite.Math. Comp., accepted, 1999, 1-21. |
| Reference:
|
[3] Gauss C. P.: Disquisitiones arithmeticae.Springer, Berlin 1986. Zbl 0585.10001, MR 0837656 |
| Reference:
|
[4] Inkeri K.: Tests for primality.Ann. Acad. Sci. Fenn. Ser. A I No. 279 1960, 1-19. Zbl 0092.27506, MR 0117202 |
| Reference:
|
[5] Jones R,, Pearce J.: A postmodern view of fractions and the reciprocals of Fermat primes.Math. Mag. 73, 2000, 83-97. MR 1822751, 10.2307/2691078 |
| Reference:
|
[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 1316595 |
| Reference:
|
[7] Křížek M., Luca F., Somer L.: 17 lectures on the Fermat numbers. From number theory to geometry.Springer-Verlag, New York 2001. MR 1866957 |
| Reference:
|
[8] Křížek M., Somer L.: A necessary and sufficient condition for the primality of Fermat numbers.Math. Bohem. 126, 2001, 541-549. MR 1970256 |
| Reference:
|
[9] Luca F.: Fermat numbers and Heron triangles with prime power sides.Amer. Math. Monthly, accepted in 2000. |
| Reference:
|
[10] Lucas E.: Theoremes d'arithmétique.Atti della Reale Accademia delle Scienze di Torino 13, 1878, 271-284. |
| Reference:
|
[11] Mcintosh R.: A necessary and sufficient condition for the primality of Fermat numbers.Amer. Math. Monthly 90, 1983, 98-99. Zbl 0513.10012, MR 0691180, 10.2307/2975806 |
| Reference:
|
[12] Morehead J. C.: Note on Fermat's numbers.Bull. Amer. Math. Soc. 11, 1905, 543-545. MR 1558255, 10.1090/S0002-9904-1905-01255-6 |
| Reference:
|
[13] Pepin P.: Sur la formule $2^{2^n} + 1$.C. R. Acad. Sci. 85, 1877, 329-331. |
| Reference:
|
[14] Somer L., Křížek M.: On a connection of number theory with graph theory.Czechoslovak Math. J. (submitted) MR 2059267 |
| Reference:
|
[15] Szalay L.: A discrete iteration in number theory.(Hungarian), BDTF Tud, Kozi. VIII. Termeszettudomanyok 3., Szombathely, 1992, 71-91. Zbl 0801.11011 |
| Reference:
|
[16] Vasilenko O. N.: On some properties of Fermat numbers.(Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh., no. 5 1998, 56-58. Zbl 1061.11500, MR 1708238 |
| Reference:
|
[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. |
| . |
