References: [ Home | Author index | Key index | Search ]

Item(s) in original BibTeX format

@unpublished{Shevelev2008,
  AUTHOR =       {V. Shevelev},
  TITLE =        {Overpseudoprimes, {M}ersenne numbers and {W}ieferich primes},
  NOTE =         {avaliable from \url{http://arxiv.org/abs/0806.3412}},
  year =         {2008},
  month =        {July},
  abstract =     {We introduce a new class of pseudoprimes-so called "overpseudoprimes" which is a special
  subclass of super-Poulet pseudoprimes. Denoting via $h(n)$ the multiplicative order of 2 modulo $n,$ we
  show that odd number $n$ is overpseudoprime iff value of $h(n)$ is invariant of all divisors $d>1$ of $n.$
  In particular, we prove that all composite Mersenne numbers $2^p-1,$ where $p$ is prime, and squares of
  Wieferich primes are overpseudoprimes. We give also a generalization of the results on arbitrary base $a>1$
  and prove that every overpseudoprime is strong pseudoprime of the same base.}
}