5 problems

Let $N$ be an odd perfect number in Eulerian form … where $p$ is the special prime. Descartes–Frenicle–Sorli conjecture. The exponent satisfies $k=1$. This conjecture concerns the…

Prime-value conjecture. Then $t=2^r-1$ is prime. The claim is presented as a natural prediction in the paper's discussion of remaining cases; it is not resolved there and is intend…

Let $m=q^k n^2$ be an odd perfect number in Eulerian form, where $q$ is the special prime satisfying $q\equiv k\equiv 1\pmod 4$ and $\gcd(q,n)=1$. Descartes–Frenicle conjecture. Th…

An $n$-obstruction is a set of primes greater than $3$, $a_i,b_i,c_i$ for $1\leq i\leq n$, together with an odd prime $p$, such that, for every $i$,…

Let $E$ be the set of numbers of Euler's form for an odd perfect number, and for real numbers $\alpha$ and $\beta$ let $OR_{\alpha,\beta}$ denote the property…