Michal Krizek, Mathematical Institute, Academy of Sciences, Zitna 25, CZ-115 67 Praha 1, Czech Republic, e-mail: krizek@math.cas.cz; Lawrence Somer, Department of Mathematics, Catholic University of America, Washington, D.C. 20064, U.S.A., e-mail: somer@cua.edu
Abstract: We examine primitive roots modulo the Fermat number $F_m=2^{2^m}+1$. We show that an odd integer $n\ge3$ is a Fermat prime if and only if the set of primitive roots modulo $n$ is equal to the set of quadratic non-residues modulo $n$. This result is extended to primitive roots modulo twice a Fermat number.
Keywords: Fermat numbers, primitive roots, primality, Sophie Germain primes
Classification (MSC 2000): 11A07, 11A15, 11A51
Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
