5 problems

Let $a\geqslant 3$ be an odd integer, and let $\langle a,a+2\rangle$ denote the numerical semigroup generated by $a$ and $a+2$. Let $(u_n)_{n\geqslant 1}$ be the recursive sequence…

Large-shift infinite square-sequence conjecture. If $a>30$, then

Let $p$ be a prime, let $(K,\mathcal{O},k)$ be a $p$-modular system, and let $B$ be a block of $\mathcal{O}G$ for a finite group $G$. The strong $\mathcal{O}$-Frobenius number…

Let $R_n^k$, with $n=T_km+j$, be a numerical semigroup given by its minimal relations on the residue class of $n$ modulo $T_k$: … If $k=2q$, the polynomials $E_{ij}^{(k)}(m)$ have…

Frobenius discrepancy conjecture for three generators.