8 problems

Extended congruence system conjecture. For every prime $p$, there exist $d,n\in\mathbb{N}$ such that at least one of these three congruences holds. If true, this congruence system…

Complete congruence system conjecture. For every prime $p$, there exist $d,n\in\mathbb{N}$ such that at least one of these congruences holds. If true, this congruence system covers…

The Erdős–Straus conjecture asks whether every integer $p>1$ admits a decomposition … with positive integers $x,y,z$. A solution is said to be of Type A or B when it has the corres…

Type I(b) existence conjecture. Every prime $p$ has a type I(b) solution.

Exceptional-prime conjecture. The only prime $p$ for which there is no type I(a) solution is $p=193$.

Let $\mathcal{N}_1$ be the set defined earlier in the paper, and let the three sets in the conjecture be the sets displayed immediately after the statement in the source. The $q$-s…

For each $q e 0$ in $mathbb{Z}{0}$, consider the three relations … … and … where $(x,y,z)\in\mathbb{Z}_{\ge 0}^3$ and $q(x,y,z)$ is the polynomial defined in the paper. The $q$-co…

Let $p(x,y,z)$ be the polynomial introduced in the paper, whose values at nonnegative integers are used to produce numbers satisfying the Erdős–Straus conjecture. Polynomial-value…