A positive integer is the form of 3q+1 q, being a natural number. Can you write its square in any form other than 3m+1 i.e. 3m or 3m+2 for some integer? Justify your answer.

Explanation

To solve the problem, we need to analyze the square of a positive integer of the form \(3q + 1\) where \(q\) is a natural number. We will determine whether its square can be expressed in the forms \(3m\) or \(3m + 2\) for some integer \(m\).

### Step-by-Step Solution:

1. **Define the Positive Integer**:
Let \(a = 3q + 1\), where \(q\) is a natural number.

2. **Square the Integer**:
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