Overpseudoprimes, Mersenne Numbers and Wieferich Primes
نویسنده
چکیده
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 if and only if the value of h(n) is invariant of all divisors d > 1 of n. In particular, we prove that all composite Mersenne numbers 2 − 1, where p is prime, and squares of Wieferich primes are overpseudoprimes.
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تاریخ انتشار 2008