2025/04/09 by Chen, Jiayu, Jin, Jing, Yao, Olivia X. M.
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2504.06941
Let bt(n) denote the number of overcubic partition triples of n. Nayaka, Dharmendra and Kumar proved some congruences modulo 8, 16 and 32 for bt(n). Recently, Saikia and Sarma established some congruences modulo 64 for bt(n) by using both elementary techniques and the theory of modular forms. In their paper, they also posed two conjectures on infinite families of congruences modulo 64 and 128 for bt(n). In this paper, we confirm the two conjectures.