(untitled) (Communications in Mathematical Research, 2019)
Let E(a, f) be the set of a-points of a meromorphic function f(z) counting multiplicities. We prove that if a transcendental meromorphic function f(z) of hyper order strictly less than 1 and its nth exact difference Δ_c^nf(z) satisfy E(1, f)=E(1, Δ_c^nf), E(0, f)E(0, Δ_c^nf) and E(∞, f)E(∞, Δ_c^nf), then Δ_c^nf(z)f(z). This result improves a more recent theorem due to Gao et al. (Gao Z, Kornonen R, Zhang J, Zhang Y. Uniqueness of meromorphic functions sharing values with their nth order exact differences. Analysis Math., 2018, https://doi.org/10.1007/s10476018-0605-2) by using a simple method.