On Fermat numbers
Pokroky matematiky, fyziky a astronomie (1995)
- Volume: 40, Issue: 5, page 243-253
- ISSN: 0032-2423
Access Full Article
topHow to cite
topKřížek, Michal. "O Fermatových číslech." Pokroky matematiky, fyziky a astronomie 40.5 (1995): 243-253. <http://eudml.org/doc/35970>.
@article{Křížek1995,
author = {Křížek, Michal},
journal = {Pokroky matematiky, fyziky a astronomie},
keywords = {Fermat numbers; greatest common divisor},
language = {cze},
number = {5},
pages = {243-253},
publisher = {Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists},
title = {O Fermatových číslech},
url = {http://eudml.org/doc/35970},
volume = {40},
year = {1995},
}
TY - JOUR
AU - Křížek, Michal
TI - O Fermatových číslech
JO - Pokroky matematiky, fyziky a astronomie
PY - 1995
PB - Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists
VL - 40
IS - 5
SP - 243
EP - 253
LA - cze
KW - Fermat numbers; greatest common divisor
UR - http://eudml.org/doc/35970
ER -
References
top- Brent, R. P., Factorization of the eleventh Fermat number, Abstracts Amer. Math. Soc. 10 (1989), 176–177. (1989)
- Brent, R. P., Pollard, J. M., Factorization of the eighth Fermat number, Math. Comp. 36 (1981), 627–630. (1981) Zbl0476.10007MR0606520
- Brillhart, J., Lehmer, D. H., Selfridge, J. L., Tuckerman, B., Wagstaff, S. S., Factorization of , up to high powers, Contemporary Math. vol. 22, Amer. Math. Soc., Providence 1988. (1988) MR0996414
- Crandall, R., Doenias, J., Norrie, C., Young, J., The twenty-second Fermat number is composite, Math. Comp. 64 (1995), 863–868. (1995) Zbl0823.11073MR1277765
- Dickson, L. E., History of the theory of numbers: Divisibility and primality, Carnegie Inst. of Washington 1919. (1919) Zbl47.0100.04
- Gostin, G. B., McLaughlin, P. B., Jr.,, Six new factors of Fermat numbers, Math. Comp. 38 (1982), 645–649. (1982) Zbl0486.10005MR0645680
- Hardy, G. H., Wright, E. M., An introduction to the theory of numbers, Clarendon Press, Oxford 1945. (1945)
- Keller, W., Factors of Fermat numbers and large primes of the form , Math. Comp. 41 (1983), 661–673. (1983) MR0717710
- Keller, W., Factors of Fermat numbers and large primes of the form . II, Preprint Univ. of Hamburg (1992), 1-40. (1992)
- Křížek, M., Chleboun, J., A note on factorization of the Fermat numbers and their factors of the form , Math. Bohem. 119 (1994), 437–445. (1994) Zbl0822.11007MR1316595
- Lenstra, H. W., Factoring integers with elliptic curves, Ann. of Math. 126 (1987), 649–673. (1987) Zbl0629.10006MR0916721
- Lenstra, A. K., Lenstra, H. W., Jr., Manasse, M. S., Pollard, J. M., The factorization of the ninth Fermat number, Math. Comp. 61 (1993), 319–349. (1993) Zbl0792.11055MR1182953
- Lenstra, H. W., Pomerance, C., A rigorous time bound for factoring integers, J. Amer. Math. Soc. 5 (1992), 483–516. (1992) Zbl0770.11057MR1137100
- Ligh, S., Jones, P., Generalized Fermat and Mersenne numbers, Fibonacci Quart. 20 (1982), 12–16 . (1982) Zbl0477.10017MR0660752
- Montgomery, P. L., New solutions of , Math. Comp. 61 (1993), 361–363. (1993) MR1182246
- Morrison, M. A., Brillhart, J., A method of factoring and factorization of , Math. Comp. 29 (1975), 183–205. (1975) Zbl0302.10010MR0371800
- Pollard, J. M., Theorems on factorization and primality testing, Math. Proc. Cambridge Philos. Soc. 76 (1974), 521–528. (1974) Zbl0294.10005MR0354514
- Pudlák, P., O složitosti, PMFA 33 (1988), 20–34. (1988)
- Reisel, H., Prime numbers and computer methods for factorization, Birkhäuser, Boston-Basel-Stuttgart 1985. (1985) MR0897531
- Robinson, R. M., The converse of Fermat’s theorem, Amer. Math. Monthly 64 (1957), 703–710. (1957) Zbl0079.06303MR0098057
- Schroeder, M. R., Number theory in science and communication, Springer-Verlag 1990. (1990) Zbl0781.11043
- Sierpiński, W., Teorija liczb, Warszawa 1950. (1950)
- Skula, L., Některé historické aspekty Fermatova problému, PMFA 39 (1994), 318–330. (1994)
- Stewart, I., Geometry finds factors faster, Nature 325 (1987), 199. (1987)
- Šalát, T., O dokonalých číslach, PMFA IX (1964), 1–13. (1964)
- Šofr, B., Euklidovské geometrické konštrukcie, ALFA, Bratislava 1976. (1976)
- Young, J., Buell, D. A., The twentieth Fermat number is composite, Math. Comp. 50 (1988), 261–263. (1988) Zbl0633.10001MR0917833
- Williams, H. C., How was factored?, Math. Comp. 61 (1993), 463–474. (1993) MR1182248
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.