| Title:
|
O Fermatových číslech (Czech) |
| Title:
|
On Fermat numbers (English) |
| Author:
|
Křížek, Michal |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
40 |
| Issue:
|
5 |
| Year:
|
1995 |
| Pages:
|
243-253 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11-04 |
| MSC:
|
11A51 |
| MSC:
|
11Y05 |
| idZBL:
|
Zbl 0863.11003 |
| idMR:
|
MR1386144 |
| . |
| Date available:
|
2010-12-11T14:00:05Z |
| Last updated:
|
2012-08-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/138304 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Brillhart, J., Lehmer, D. H., Selfridge, J. L., Tuckerman, B., Wagstaff, S. S.: Factorization of $b^n\pm 1$, $b=2,3,5,6,7,10,11,12$ up to high powers.Contemporary Math. vol. 22, Amer. Math. Soc., Providence 1988. MR 0996414 |
| Reference:
|
[4] Crandall, R., Doenias, J., Norrie, C., Young, J.: The twenty-second Fermat number is composite.Math. Comp. 64 (1995), 863–868. Zbl 0823.11073, MR 1277765 |
| Reference:
|
[5] Dickson, L. E.: History of the theory of numbers: Divisibility and primality.Carnegie Inst. of Washington 1919. |
| Reference:
|
[6] Gostin, G. B., McLaughlin, P. B., Jr., : Six new factors of Fermat numbers.Math. Comp. 38 (1982), 645–649. Zbl 0486.10005, MR 0645680 |
| Reference:
|
[7] Hardy, G. H., Wright, E. M.: An introduction to the theory of numbers.Clarendon Press, Oxford 1945. |
| Reference:
|
[8] Keller, W.: Factors of Fermat numbers and large primes of the form $k\cdot 2^n+1$.Math. Comp. 41 (1983), 661–673. MR 0717710 |
| Reference:
|
[9] Keller, W.: Factors of Fermat numbers and large primes of the form $k\cdot 2^n+1$. II.Preprint Univ. of Hamburg (1992), 1-40. |
| Reference:
|
[10] 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:
|
[11] Lenstra, H. W.: Factoring integers with elliptic curves.Ann. of Math. 126 (1987), 649–673. Zbl 0629.10006, MR 0916721 |
| Reference:
|
[12] 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. Zbl 0792.11055, MR 1182953 |
| Reference:
|
[13] Lenstra, H. W., Pomerance, C.: A rigorous time bound for factoring integers.J. Amer. Math. Soc. 5 (1992), 483–516. Zbl 0770.11057, MR 1137100 |
| Reference:
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[14] Ligh, S., Jones, P.: Generalized Fermat and Mersenne numbers.Fibonacci Quart. 20 (1982), 12–16 . Zbl 0477.10017, MR 0660752 |
| Reference:
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[15] Montgomery, P. L.: New solutions of $a^{p-1}\equiv 1 (\operatorname{mod} p)^2$.Math. Comp. 61 (1993), 361–363. MR 1182246 |
| Reference:
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[16] Morrison, M. A., Brillhart, J.: A method of factoring and factorization of $F_7$.Math. Comp. 29 (1975), 183–205. MR 0371800 |
| Reference:
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[17] Pollard, J. M.: Theorems on factorization and primality testing.Math. Proc. Cambridge Philos. Soc. 76 (1974), 521–528. Zbl 0294.10005, MR 0354514 |
| Reference:
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[18] Pudlák, P.: O složitosti.PMFA 33 (1988), 20–34. |
| Reference:
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[19] Reisel, H.: Prime numbers and computer methods for factorization.Birkhäuser, Boston-Basel-Stuttgart 1985. MR 0897531 |
| Reference:
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[20] Robinson, R. M.: The converse of Fermat’s theorem.Amer. Math. Monthly 64 (1957), 703–710. Zbl 0079.06303, MR 0098057 |
| Reference:
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[24] Stewart, I.: Geometry finds factors faster.Nature 325 (1987), 199. |
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[25] Šalát, T.: O dokonalých číslach.PMFA IX (1964), 1–13. |
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| Reference:
|
[28] Williams, H. C.: How was $F_6$ factored?.Math. Comp. 61 (1993), 463–474. MR 1182248 |
| . |
