Write whether the square of any positive integer can be of the form 3m+2, where m is a natural number. Justify answer.

Explanation

To determine whether the square of any positive integer can be of the form \(3m + 2\) (where \(m\) is a natural number), we can analyze the squares of integers based on their remainders when divided by 3.

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to check if \(n^2\) (where \(n\) is a positive integer) can be expressed in the form \(3m + 2\).

2. **Using Euclid's Division Lemma**: According to Euclid's division lemma, any integer \(n\) can be expressed as:
\[
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