In this paper, we investigate the uniqueness problem of entire functions sharing two polynomials with their k-th derivatives. We look into the conjecture given by Lü, Li and Yang [Bull. Korean Math. Soc., 51(2014), 1281–1289] for the case F = fⁿP(f), where f is a transcendental entire function and P(z) = a_mz^m+a_m−1z^m−1+ …+a₁z+a₀(≢ 0), m is a nonnegative integer, a_m, a_m−1, …, a₁, a₀ are complex constants and obtain a result which improves and generalizes many previous results. We also provide some examples to show that the conditions taken in our result are best possible.

Keywords: entire function, derivative, uniqueness.