# Journal of the Ramanujan Mathematical Society

Volume 34, Issue 4, December 2019 pp. 417–426.

New Infinite Families of Congruences Modulo 3, 5 and 7 for Overpartition Function

**Authors**:
Jubaraj Chetry and Nipen Saikia

**Author institution:**Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791 112, Arunachal Pradesh, India

**Summary: **
Let p (n) denote the number of overpartitions of a
non-negative integer n. In this paper, we prove two new infinite
families of congruences modulo 3 for p (n) by using
Ramanujan's theta-function identities. Particularly, we prove
that, for any integer α ≥ 0,
p (9 α +1(24n+23)) ≡ 0 (mod 3) and
p (9 α +1(24n+22)+1) ≡ 0 (mod 3). Furthermore, we
prove some new congruences modulo 5 and 7 for p (n). For
example, we prove that p (5n+k+3) ≡ 0 (mod 5), where
k = 3n2 ± n.

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