4 problems

Let $f\in\mathbb{Z}[x]$ be a quadratic polynomial. Call $f$ stable if every iterate $f^n$ is irreducible over $\mathbb{Q}$, and call $f$ critically infinite if the forward orbit of…

Let $\mathcal{ML}$ be the set of primes $p$ for which the Marques–Lengyel conjecture holds, and let $\mathcal{NMLR}$ be the set of primes for which the rational-center variant fail…

Density conjecture. The density of primes $p$ for which $\operatorname{gcd}(\#E(\mathbb{F}_p),p-1)=1$ is

For integers $e,f$ with $1\le e\le f$ and $e+f\ge 3$, let ${\mathcal Q}_w(e,f)$ be the set of primes occurring in a weak Carmichael number of the form $p^eq^f$ or $q^ep^f$ for some…