3 problems

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…