# Are you smarter than an 8th grader? #3

**Number Theory**Level pending

This problem is part of the question set Mathematics in Anime. It appears in the anime *Puella Magi Madoka Magica*. Students attending the Math class are only \(14\) years old, yet they are expected to solve the following problem on the spot!

The integer solutions of the equation \(a^{3}+a^{2}-ab+b-1=0\) can be expressed in \((a_1, b_1), (a_2, b_2), \ldots (a_n, b_n)\).

Find \( \sum_{i=1}^n (a_i+b_i)\)

Image and translation credits: Puella Magi Wiki