Bulletin of the
Korean Mathematical Society BKMS

In this paper, we study the uniqueness of entire functions and prove the following result: Let $f(z)$ and $g(z)$ be two nonconstant entire functions, $n\ge 7$ a positive integer, and let $a$ be a nonzero finite complex number. If $f^{n}(z)(f(z)-1)f'(z)$ and $g^{n}(z)(g(z)-1)g'(z)$ share $a$ CM, then $f(z)\equiv g(z)$. The result improves the theorem due to ref. [3].

Keywords: entire function, sharing value, uniqueness

MSC numbers: 30D35