MathDB

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?

Problem Statement