3 problems

Relatively Prime Conjecture. For all such ${\bf a},{\bf b}$ and all $n\in\mathbb N$, the polynomials $P_{{\bf a},{\bf b},n}(X)$ and $P_{{\bf a},{\bf b},n+1}(X)$ have no common zero…

Strong Factorial Conjecture. $F_\cap^{[m]}={\mathbb C}^{[m]}$; equivalently, every polynomial belongs to the strong factorial set. This conjecture is explicitly stated as stronger…

Factorial Conjecture. For all $f\in{\mathbb C}^{[m]}$,