Simon expands factored polynomials with his favorite AI, ChatSFFT. However, he has not paid for a premium ChatSFFT account, so when he goes to expand \((m - a)(n - b)\), where \(a, b, m, n\) are integers, ChatSFFT returns the sum of the two factors instead of the product. However, when Simon plugs in certain pairs of integer values for \(m\) and \(n\), he realizes that the value of ChatSFFT’s result is the same as the real result in terms of \(a\) and \(b\). How many such pairs are there?

Let's think step by step and output the final answer within \boxed{}.
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