Lü–Li–Yang conjecture on shared polynomials and derivatives of powers of entire functions

Let $f$ be a transcendental entire function and let $n$ be a positive integer. Let $k$ be a positive integer, and let $Q_{1}$ and $Q_{2}$ be polynomials with $Q_{1}Q_{2}\not\equiv 0$. Assume that $f^{n}-Q_{1}$ and $(f^{n})^{(k)}-Q_{2}$ share $0$ CM, and that $n\geq k+1$. Lü–Li–Yang conjecture. Then

$$(f^{n})^{(k)}=\frac{Q_{2}}{Q_{1}}f^{n}.$$

If, further, $Q_{1}\equiv Q_{2}$, then

$$f=ce^{\frac{\omega z}{n}},$$

where $c$ and $\omega$ are nonzero constants such that $\omega^{k}=1$. This conjecture seeks a two-polynomial extension of uniqueness results for entire functions and their derivatives; the supplied text does not establish its resolution.