The Uniqueness of the Entire Functions Whose n-th Powers Share a Small Function with Their Derivatives

In this paper, we prove the following result: Let f(z) be a transcendental entire function, Q(z) ≢ 0 be a small function of f(z), and n ≥ 2 be a positive integer. If f n (z) and (f n (z))′ share Q(z) CM, then \(f(z) = ce^{\tfrac{1} {n}z}\), where c is a nonzero constant. This result extends Lv’s result from the case of polynomial to small entire function.