In 2011, Heittokangas et al. (Complex Var Ellipt Equat 56(1–4):81–92, 2011) proved that if a non-constant finite order entire function f(z) and f(z+η)\documentclass[12pt]{minimal}
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\begin{document}$$f(z+\eta )$$\end{document} share a, b, c IM, where η\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document} is a finite non-zero complex number, while a, b, c are three distinct finite complex values, then f(z)=f(z+η)\documentclass[12pt]{minimal}
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\begin{document}$$f(z)=f(z+\eta )$$\end{document} for all z∈C\documentclass[12pt]{minimal}
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\begin{document}$$z\in \mathbb {C}$$\end{document}. We prove that if a non-constant finite order entire function f and its n-th difference operator Δηnf\documentclass[12pt]{minimal}
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\begin{document}$$\Delta ^n_{\eta }f$$\end{document} share a1\documentclass[12pt]{minimal}
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\begin{document}$$a_1$$\end{document}, a2\documentclass[12pt]{minimal}
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\begin{document}$$a_2$$\end{document}, a3\documentclass[12pt]{minimal}
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\begin{document}$$a_3$$\end{document} IM, where n is a positive integer, η≠0\documentclass[12pt]{minimal}
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\begin{document}$$\eta \ne 0$$\end{document} is a finite complex value, while a1\documentclass[12pt]{minimal}
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\begin{document}$$a_1$$\end{document}, a2\documentclass[12pt]{minimal}
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\begin{document}$$a_2$$\end{document}, a3\documentclass[12pt]{minimal}
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\begin{document}$$a_3$$\end{document} are three distinct finite complex values, then f=Δηnf\documentclass[12pt]{minimal}
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\begin{document}$$f=\Delta ^n_{\eta }f$$\end{document}. The main results in this paper also improve Theorems 1.1 and 1.2 from Li and Yi (Bull Korean Math Soc 53(4):1213–1235, 2016).
