Entire functions that share a polynomial with their derivatives

Let f be a nonconstant entire function, k and q be positive integers satisfying k>q, and let Q be a polynomial of degree q. This paper studies the uniqueness problem on entire functions that share a polynomial with their derivatives and proves that if the polynomial Q is shared by f and f′ CM, and if f(k)(z)−Q(z)=0 whenever f(z)−Q(z)=0, then f≡f′. We give two examples to show that the hypothesis k>q is necessary.