Fermat and mersenne numbers in Pepin's test

• Autorzy: Solcova A. , Krizek M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Fermat primes; Mersenne numbers; Pepin's test; primitive roots

PL

liczby Fermata; liczby Mersenne'a; test Pepins'a

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 4
• Strony: 737--742
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Solcova A.

autor

Krizek M.

• Department of Mathematics Faculty of Civil Engineering The Czech Technical University, Thakurova 7, Cz-166 29 Prague 6, Czech Republic,

Bibliografia

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• [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.