On Mersenne polynomials over F2

Abstract We work over the field with two elements. We establish a new correspondence between Mersenne polynomials and trinomials so that corresponding polynomials have the same number of irreducible factors. This allows us to get a partial but nontrivial result about the factorization of M 2 h + 1 + 1 , for a Mersenne prime M and for a positive integer h .