7 problems

Let $A$ be the coefficient ring and let … be a Drinfeld module. For each prime polynomial $P$, let $g_{P,\phi}$ denote the auxiliary polynomial associated with $P$ and $\phi$. Prim…

Gall-Rahav conjecture. The polynomial $\sigma(M^{2h})$ is divisible by a non-Mersenne prime.

Let $\rho$ be a prime and let $M_\rho=2^\rho-1$. The Mersenne-prime residue conjecture. If $M_\rho$ is a Mersenne prime, then exactly one of the following holds:…

Let $A$ be an even nonsplitting perfect polynomial over $\mathbb{F}_2$, and consider its odd divisors. A prime is called Mersenne or 2-Mersenne according to the terminology of the…

Let $S$ be a 2-Mersenne prime and let $h\geq 2$. The polynomial sum-of-divisors function is denoted by $\sigma$. 2-Mersenne divisor conjecture. The integer $\sigma(S^{2h})$ is divi…

Let $M$ be a Mersenne prime and let $h\geq 2$. The polynomial sum-of-divisors function is denoted by $\sigma$. Mersenne divisor conjecture. The integer $\sigma(M^{2h})$ is divisibl…

A positive integer $n$ is near-perfect if it is the sum of all its proper divisors except one proper divisor, called its redundant divisor. The number $n$ is even when it is divisi…