On the least primitive root modulo 2p for odd primes p

• Autorzy: Paszkiewicz A.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present results of numerical investigations concerning primitive roots modulo m = 2p, where p is prime greater than 2. This is one of these cases of integers m for which the multiplicative group of primitive rests modulo m can be generated by one element. Our computations comprise all primes below 10 ¹⁰ .

Słowa kluczowe

EN

multiplicative group modulo an integer m; least primitive root; cyclic groups; generator of a group

PL

programowanie całkowitoliczbowe; arytmetyka modulo; multiplikatywna grupa modulo; pierwiastki pierwotne; grupy cylkiczne

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: Electronics and Telecommunications Quarterly
• Rocznik: 2009
• Tom: Vol. 55, No 4
• Strony: 649--658
• Opis fizyczny: Bibliogr. 4 poz., tab., wykr.

Twórcy

autor

Paszkiewicz A.

• Warsaw University of Technology

Bibliografia

• 1. K. Ireland, M. Rosen: A Classical Introduction to modem Number Theory, Springer-Verlag, New York, Heidelberg, Berlin, 1982, Graduate Texts in Mathematics, 87.
• 2. A. Paszkiewicz, A. Schinzel: On the least prime primitive root modulo a prime, Math. Comp. v. 71, no. 239, pp. 1307-1321, 2002.
• 3. A. Paszkiewicz: On least primitive roots mod 2p for odd primes, Electronics and Telecommunications Quarterly, 55, no. 1, pp. 57-69, 2009.
• 4. A. Paszkiewicz: A new prime p for which the lest primitive root (mod p) and the least primitive root (mod p2) are not equal, Math. Comp., v.78, no. 266, pp. 1193-1195, Apr. 2009.