3 problems

Let $\Lambda$ be the formal recursion operator and suppose it has the form described in the paper, with $\phi(\xi_1)$ a rational function and $\omega(\xi_1)$ a Laurent polynomial.…

Chen et al.'s conjecture. The conclusion that every such solution satisfies $\rho(f)=\deg(Q)=1$ also holds for $n=2$.

Rong and Xu's conjecture. Case (iii) can be removed when $N(r,1/f)=S(r,f)$ for $n=2,3$.