CONGRUENCES FOR BIPARTITIONS WITH ODD DESIGNATED SUMMANDS
M. S. Mahadeva Naika, T. Harishkumar, Mukesh Prasad, T. N. Veeranayaka · South East Asian J of Mathematics and Mathematical Sciences · 2023
Andrews, Lewis and Lovejoy investigated a new class of partitions with designated summands by taking ordinary partitions and tagging exactly one of each part size. Let B2(n) count the number of bipartitions of n with designated summands in which all parts are odd. In this work, we establish many infinite families of congruences modulo powers of 2 and 3 for B2(n). For example, for each n > 0 and Alpha > 0, B2 ???? 48 · 52Alpha+2n + a1 · 52Alpha+1 ≡ 0 (mod 9), where a1 ∈ {88, 136, 184, 232}.