Uniqueness on entire functions and their nth order exact differences with two shared values

Abstract

Abstract Let f(z) be an entire function of hyper order strictly less than 1. We prove that if f(z) and its nth exact difference Δ c n f ( z ) {\Delta }_{c}^{n}f(z) share 0 CM and 1 IM, then Δ c n f ( z ) ≡ f ( z ) {\Delta }_{c}^{n}f(z)\equiv f(z) . Our result improves the related results of Zhang and Liao [Sci. China A, 2014] and Gao et al. [Anal. Math., 2019] by using a simple method.