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 Uniqueness theorem for a meromorphic function and its exact difference Bull. Korean Math. Soc.Published online July 31, 2020 Shengjiang Chen and Aizhu Xu Ningde Normal University Abstract : Let $f(z)$ be a non-constant meromorphic function of hyper order strictly less than $1$, and let $c$ be a nonzero finite complex number such that $\Delta f(z)=f(z+c)-f(z)(\not\equiv0)$. We prove that if $f(z)$ and $\Delta f(z)$ share $0,\infty$ CM and $1$ IM, then $\Delta f(z)\equiv f(z)$. Our result generalizes and greatly improves the related results. Keywords : Meromorphic function; exact difference; uniqueness; shared values. MSC numbers : 30D35, 39A10 Full-Text :