In this study, we focus on an abstract form of summation equations, which can be regarded
as a particular class of nonlinear difference equations. We investigate sufficient conditions for
the existence of discrete almost automorphic solutions by appealing to the fixed point theory and
establish a linkage between the existence of discrete almost automorphic solutions and the existence
of bounded solutions for the nonlinear difference equations in the spotlight. Consequentially, we
propose a discrete counterpart of the Bohr-Neugebauer theorem for the qualitative theory of difference
equations.