International Research Journal of Education and Technology

In this paper we introduce a new class of  Mersenne and Mersenne-Lucas numbers, constructed in the framework of non-Newtonian calculus, that we call respectively, non-Newtonian Mersenne and non-Newtonian Mersenne-Lucas numbers.  From the view point of non-Newtonian calculus, we investigate some important identities and formulas of the classical Mersenne numbers and Mersenne-Lucas numbers.  As a result we prove several relations of non-Newtonian Mersenne and Mersenne-Lucas numbers. We also study some other properties of these non-Newtonian numbers, such as Catalan-like identities, Cassini-like identities, Binet-like formulas and generating functions.