The uniqueness of the entire functions whose \(n\)-th powers share a small function with their derivatives (Q2453836)

The authors prove that if the \(n\)-th power (\(n\geq 2\) being a positive integer) of a transcendental entire function \(f\left( z\right) \) and its first derivative share a small function \(Q\left( z\right) \) counting multiplicities (CM), then \(f\left( z\right) \) will be of the form \(c\exp \left( \frac{z}{n}\right) \) where \(c\) is a non-zero constant. In fact, they extend a result of [\textit{F. Lü} et al., Arch. Math. 92, No. 6, 593--601 (2009; Zbl 1179.30027)] from the case of polynomials to small entire functions.