  In this paper, we investigate the sharing values problem that entire function
$f(z)$ and its first order difference operator $\Delta_{\eta}f(z)$ share two
distinct pairs of finite values IM. We prove: Let $f(z)$ be a non-constant
entire function of hyper-order less than $1$, let $\eta$ be a non-zero complex
number, and let $a$ be a nonzero finite number. Then there exists no such
entire function so that $ f(z)$ and $\Delta_{\eta}f(z)$ share $(0,0)$ and
$(a,-a)$ IM. Furthermore, using a result in Wang-Chen-Hu \cite{wch}, we obtain
some uniqueness results that when $ f(z)$ and $\Delta_{\eta}f(z)$ share
$a\neq0$ and $-a$ IM.

Complex Variables