Some properties of prime numbers of special form and Carmichael numbers

N.V. Kalashnіkova (Oles Honchar Dnipropetrovsk National University)


We study some properties of structure of the multiplicative group $$$Z^*_m$$$, in case when m is Mersenne prime, Fermat or Carmichael number. Using the results of these studies, we obtain properties of Mersenne primes, Fermat and Carmichael numbers.


Mersenne prime; Fermat prime; Carmichael number; congruence; multiplicative group


Boss V. Lectures on mathematics. Vol. 14: Number theory, URSS, Moscow, 2013; 214 p. (in Russian)

Crandall R., Pomerance C. Prime Numbers. A Computational Perspective, URSS, Moscow, 2011; 663 p. (in Russian)




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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991