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This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home  Author index  Key index  Search ]
 Shevelev2008
 V. Shevelev, "Overpseudoprimes, Mersenne numbers and Wieferich primes," (July 2008) avaliable from http://arxiv.org/abs/0806.3412.
Abstract:
We introduce a new class of pseudoprimesso called "overpseudoprimes" which is a special subclass of superPoulet 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.
