# General Family of Congruences Modulo Large Powers of 3 for Cubic Partition Pairs

### From NZJM

**New Zealand Journal of Mathematics**

**Vol.** 47, (2017), **Pages** 43-56

**D. S. Gireesh**

Department of Mathematics,

Dayananda Sagar College of Engineering,

Shavige Malleshwara Hills,

Kumaraswamy Layout,

Bengaluru-560 078, Karnataka,

India.

**M. S. Mahadeva Naika **

Department of Mathematics,

Bangalore University,

Central College Campus,

Bengaluru-560 001, Karnataka,

India.

mailto:msmnaika@rediffmail.com

**Abstract** Let *b*(*n*) denote the number of cubic partition pairs of *n*. Recently, Chern proved two of Lin's conjectures on cubic partition pairs and he asked a question about general family of congruences modulo large powers of 3 for cubic partition pairs. In this paper, we give affirmative answer to Chern's question by finding such that

In the process, we also give alternative proofs for Lin's conjectures.

**Keywords** Partitions; Cubic Partition Pairs; Congruences.

**Classification** (MSC2000) 05A17, 11P83.