Author

Kyunghwan Song

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Preprint Sep 2026

Frobenius Numbers Associated with Primitive Pythagorean Quadruples

Let $(a,b,c,d) = \left(2mn, 2mp, m^2 - n^2 - p^2, m^2 + n^2 + p^2\right)$ be a primitive Pythagorean quadruple and let $S=\langle a, b, c, d\rangle$ be the numerical semigroup generated by $a,b,c,$ and $d.$ For convenience, we also let $Q = n^2 + p^2, \delta = \gcd(n,p),$ and $n = \delta n_0$ for some $n_0 \in \mathbb{...

WonTae Hwang, Kyunghwan Song · 0 citations

Preprint Aug 2026

$p$-numerical semigroup of the sequence of consecutive odd integers

We prove the $p$-Frobenius problems proposed as Conjectures 7.1 and 7.5 developed by T. Komatsu and R. Pandey (Bull. Korean Math. Soc. 2025;62:1397--1409.) for two families of consecutive odd integers. For integers $r,L,n\ge0$, the bounded restricted partition function $p_{\le r}^{(\le L)}(\le n)$ counts partitions of...

Takao Komatsu, Sungjin Hyun, Kyunghwan Song · 0 citations