**4.** 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 . Now square each of these and show that they can be rewritten in the form 3m or 3m+1]

**Solution:**

Let x be any positive integer and b=3.

According to **Euclid's division lemma**, we can say that

Therefore, all possible values of **x** are:

or