3 problems

Minimal-period conjecture. The minimum period of $c_j(k)$ is $p_j$ for every $0\leq j\leq d$. This conjecture predicts that the divisibility data of the $a_i$ determine the exact p…

Let $r(x)$ be the generating function whose coefficients $f_{O_j}(k)$ count the relevant partitions into fractions with fixed denominator $j$, with $k$ ranging over the integer val…

Let $j>2$ and let $k,j\in\mathbb{N}$. For a sequence of numerators $\{n_j\}$, define … A sequence enables solutions when every positive integer $k<\lfloor G\rfloor$ can be represen…