So that the square of any positive integers is of the form 3m,3m+1 for

1.	So that the square of any positive integers is of the form 3m,3m+1 for some integers m
Answer» Let a be any positive integer and b = 3.Then a = 3q + r for some integer q ≥ 0And r = 0, 1, 2 because 0 ≤ r < 3Therefore, a = 3q or 3q + 1 or 3q + 2Or,a2 = (3q)2 or (3q + 1)2 or (3q + 2)2a2=9q2 or 9q2 +6q + 1 or 9q2 + 12q + 4=3 \u200b×\u200b (3q2) or 3(3q2+2q) +1 or 3(3q2+4q)+1=3k1 or 3k2+1 or 3k3+1Where k1 , k2 , and k3 are some positive integers

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