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]
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: