2025/03/24 by Tang, Dazhao
#05A15 #05A17 #11P83 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2503.18574
Let Bs,t(n) denote the number of overpartitions of n where no part is divisible by s or t, with s and t being coprime. By establishing the exact generating functions of a family of arithmetic progressions in B4,3(n), we prove that for any k≥1 and n≥1, B4,3(2k+3n)≡0\pmod23k+5. This significantly generalizes a conjectural congruence family posed by Nadji, Ahmia and Ram'ırez (Ramanujan J. 67 (1):13, 2025) recently. Moreover, we conjecture that there is an infinite family of linear congruence relations modulo high powers of 2 satisfied by B4,3(n).