Congruences for some l-regular partitions modulo l

Let bl(n)bl(n) denote the number of l-regular partitions of n. Dandurand and Penniston found numerous congruences modulo l   for bl(n)bl(n), where l∈{5,7,11}. In this paper, employing some theta function identities due to Ramanujan, we show that bl(A(k)n+B(k))≡C(k)bl(n)(modl), where A(k)A(k), B(k)B(k) and C(k)C(k) are functions in k   and l∈{13,17,19}. As corollaries of these congruences, several strange congruences for bl(n)bl(n) modulo l   are derived. For example, b19(123×510k−34)≡0(mod19).