  In this paper, we define new generalized k-Mersenne numbers and give a
formula of generalized Mersenne polynomials and further we study their
properties. Moreover, we define Gaussian Mersenne numbers and obtain some
identities like Binet Formula, Cassini's identity, D'Ocagne's Identity, and
generating functions. The generalized Gaussian Mersenne numbers are described
and the relation with classical Mersenne numbers are explained. We also
introduce a generalization of Gaussian Mersenne polynomials and establish some
properties of these polynomials.
