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On an Invariant of Divisors of Mersenne Number

where p is prime. In our paper we use the latter name. In this form numbers Mp at the first time were studied by Marin Mersenne (1588-1648) at least in 1644 (see in [1, p.9] and a large bibliography there). In our paper we show that all composite Mersenne numbers belong to a class S of pseudoprimes of base 2 which is a subclass of super-Poulet pseudoprimes. Analysis of properties of pseudoprimes from S leads us to the following result (we denote ordn2 the order of 2 (modn)). Theorem 1. Let p be a prime and d|Mp, d > 1. Then ordd 2 = p .