#### 1. Introduction

This commentary is intended to correct the errors that happened in [1]. Recall that a partition of a positive integer is a nonincreasing sequence of positive integers whose sum is . A bipartition of a positive integer is a pair of partitions such that the sum of all the parts is . Let be the number of bipartitions of . This function has some beautiful arithmetic properties (see, e.g., [2]). Recently, there is more and more research on the bipartitions with certain restrictions on each partition, for example, [37]. In this short review, we consider the number of bipartitions with the restriction that each part of is divisible by . Let denote the number of bipartitions of such that part of is divisible by . The generating function for is given by [8] where

We will mainly focus on the case when , where is any positive integer. In [1], the discussion on congruence identities for was based on an incorrect lemma. We will point out all the incorrect points in that paper in the next section.

#### 2. Comments on the Results of Saikia and Boruah

In [1], Saikia and Boruah considered the congruence identities for by employing the following lemma.

Lemma 13 of [1] where is the Rogers-Ramanujan continued fraction and

However, the lemma of this version is wrong, The correct version should be as follows.

Lemma 1. Let be defined as above:

There are several proofs of this famous identity (see, e.g., [9, 10]).

In [1], all the discussion in Section was based on Lemma of [1] which has been shown above.

Since Lemma of [1] is not correct, the discussion in Section is not correct.

First, we can say that the conclusion shown in Theorem of [1], which says is correct. However, in the course of the proof, there is one mistake. The equation which is equation () of [1], is not correct. It should be

The first result of Theorem of [1] is also correct, but the proof has a problem. In the course of the proof, equation () of [1] should be rather than

However, the second conclusion and the third conclusion of Theorem of [1] are not correct. The proof of Theorem (ii, iii) of [1] relies on the claim that However, as we have pointed out above, we do not have the factor in . This is the reason why the second conclusion and the third conclusion of Theorem of [1] cannot hold.

Actually, we do have some 3-dissection formulas to find how and modulo-3 look like. Let us show them now.

Thanks to [11], we have If we let , and in Entry 31 of [12, p. 48], we can obtain where According to these two formulas, we get that When extracting terms involving , dividing by and replacing by , we obtain When extracting terms involving , dividing by and replacing by , we obtain Up to now, we have obtained the forms of and modulo-3. However, we cannot get any congruence properties of or by the forms of and modulo-3 above.

#### Conflicts of Interest

The author declares no conflicts of interest.