$$a$$, $$b$$ are positive integers. A is the set of all divisors of $$a$$ except for $$a$$. B is the set of all divisors of $$b$$. If $$A = B$$ then which of the following is a wrong statement?

Since $$b \in B = A$$, $$b$$ is a proper divisor of $$a$$, so $$b < a$$, $$a$$ is a multiple of $$b$$, and $$b$$ is not a multiple of $$a$$. Also every proper divisor of $$a$$ must divide $$b$$. If $$a$$ had two different prime factors $$p$$ and $$q$$, then both $$\frac{a}{p}$$ and $$\frac{a}{q}$$ would divide $$b < a$$, forcing $$a$$ to divide $$b$$, which is impossible; so $$a = p^k$$, $$b = p^{k - 1}$$, and $$\frac{a}{b} = p$$ is prime. All four statements are true, so none of them is wrong.