2025/04/30 by Ghoshal, Suparno, Jana, Arijit · 2 citations
#05A15 #05A17 #11P83 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2504.21439
Recently there has been quite a bit of study carried out related to arithmetic properties of overpartitions into non-multiples of two co-prime integers. The paper [19] by Nadji et al. looked into congruences modulo 3 and powers of 2 for certain specific pairs of co-prime integers, while the paper [1] by Alanazi et al. investigated some congruences related to some similar and some different pairs of co-prime integers. In this paper we propose some elegant and elementary proofs of a subset of the congruences given in [1] by using only theta function and dissection identities. We also propose a generic method for proving congruences modulo 8 which doesn't necessarily use any specific 2-dissection.