Arithmetic properties of �-regular overpartition pairs

In this paper, we investigate the arithmetic properties of � -regular overpartition pairs. Let B�(n) denote the number of � -regular overpartition pairs of n. We will prove the number of Ramanujan-like congruences and infinite families of congruences modulo 3, 8, 16, 36, 48, 96 for B3(n) and modulo 3, 16, 64, 96 for B4(n) . For example, we find that for all nonnegative integers α and n, B3(3α(3n + 2)) � 0 (mod 3), B3(3α(6n + 4)) � 0 (mod 3), and B4(8n + 7) � 0 (mod 64). © T�BI�TAK