Use Euclid's division lemma to show that the square of any positive integer is either of the form `3m`or `3m+1`for some integer `m`.[Hint: Let x be any positive integer then it is of the form `3q`, `3q+1`or `3q+2`Now square each of these and show that they can be rewritten in the form `3m` or `3m + 1`].

Explanation

To show that the square of any positive integer is either of the form \(3m\) or \(3m + 1\) for some integer \(m\), we will use Euclid's division lemma.

### Step-by-Step Solution:

1. **Understanding Euclid's Division Lemma**:
According to Euclid's division lemma, for any integer \(a\) and a positive integer \(b\), there exist unique integers \(q\) (the quotient) and \(r\) (the remainder) such that:
\[
a = bq + r
...