Problem 5 Find the number of pairs of positive integers aaa and bbb such that a≤100000a\leq 100 000a≤100000 , b≤100000b\leq 100 000b≤100000 , and a3−ba3+b=b2−a2b2+a2.\frac{a^3-b}{a^3+b}=\frac{b^2-a^2}{b^2+a^2}.a3+ba3−b=b2+a2b2−a2.