Value distribution and uniqueness of difference polynomials and entire solutions of difference equations

This paper is devoted to value distribution and uniqueness problems for difference polynomials of entire functions such as f(n)(f - 1)f(z + c). We also consider sharing value problems for (z) and its shifts f(z + c), and improve some recent results of Heittokangas et al. [J. Math. Anal. Appl. 355 (2009), 352-363]. Finally, we obtain some results on the existence of entire solutions of a difference equation of the form f(n) + P(z)(Delta(c)f)(m) = Q(z).