3 problems

Fortuna's conjecture. The solution $X$ is entrywise nonnegative.

Norm-order preservation conjecture. If $b_1(C)\geq b_1(L)$, then

Let $\mathbb{F}$ be a field of order $p$, where $p$ is prime. Let $g=X^n-1$, and let $f\in\mathbb{F}[X]$ be a primitive polynomial of degree $n$. For a polynomial…