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Abstrakty
We examine Pepin’s test for the primality of the Fermat numbers Fm = 22m + 1 for m = 0, 1, 2, . . . . We show that Dm = (Fm - 1)/2 - 1 can be used as a base in Pepin’s test for m > 1. Some other bases are proposed as well.
Wydawca
Czasopismo
Rocznik
Tom
Strony
737--742
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
autor
- Department of Mathematics Faculty of Civil Engineering The Czech Technical University, Thakurova 7, Cz-166 29 Prague 6, Czech Republic, solcova@mbox.cesnet.cz
Bibliografia
- [1] A. Aigner, On prime numbers for which (almost) all Fermat numbers are quadratic nonresidues (German), Monatsh. Math. 101 (1986), 85–93.
- [2] R. E. Crandall, E. Mayer, J. Papadopoulos, The twenty-fourth Fermat number is composite, Math. Comp. 72 (2003), 1555–1572.
- [3] M. Křížek, F. Luca, L. Somer, 17 lectures on Fermat numbers: From number theory to geometry, CMS Books in Mathematics, vol. 9, Springer-Verlag, New York, 2001.
- [4] A. K. Lenstra H. W. Lenstra, Jr., M. S. Manasse, J. M. Pollard, The factorization of the ninth Fermat number, Math. Comp. 61 (1993), 319–349.
- [5] J. C. Morehead, Note on Fermat's numbers, Bull. Amer. Math. Soc. 11 (1905), 543–545.
- [6] J. C. Morehead, A. E. Western, Note on Fermat's numbers, Bull. Amer. Math. Soc. 16 (1910), 1–6.
- [7] P. Pepin, Sur la formule 22n + 1, C. R. Acad. Sci. 85 (1877), 329–331.
- [8] F. Proth, Mémoires présentés, C. R. Acad. Sci. Paris 87 (1878), 374.
- [9] O. N. Vasilenko, On some properties of Fermat numbers (Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh., no. 5 (1998), 56–58.
- [10] A. E. Western, Notes and corrections, Proc. London Math. Soc. 3(2) (1905), xxi–xxii.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0018-0002