7 problems

Let $p\ge 5$ be an odd prime, and let … where $a=\sigma\cdot prb$, $\sigma\in\lbrace -1,+1\rbrace$, $r\in\mathbb{N}$, and $b\in\mathbb{N}$ is squarefree. Let $N$ be the splitting f…

Irreducibility conjecture. If $|a|\geq 5$, then $x^{n}+ax^{m}\pm1$ is irreducible over $\mathbb{Q}$. Furthermore, there are only finitely many reducible polynomials of the form…

Logarithmic increment conjecture. One has

Brilleslyper and Schaubroeck's conjecture. The number of roots of $x^n+x^m-1$ in the interior of the unit circle is

Bremner and Ulas's conjecture. The reducibility type $(1,1,1,n-3)$ does not occur for $f(x)$.

Trinomial family conjecture. The family $\mathcal{F}$ contains at least one polynomial satisfying Property condition for $r=2$.

Three-linear-factor conjecture. There are no trinomials $x^n+A x+B$ defined over $\mathbb{Q}$ with reducibility type $(1,1,1,n-3)$.