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

Takao Komatsu, Sungjin Hyun, Kyunghwan Song

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 cons…