1984 AIME Problems/Problem 15
For each of the values , we have the equation
However, each side of the equation is a polynomial in of degree at most 3, and they have 4 common roots. Therefore, the polynomials must be equal.
Now we can plug in into the polynomial equation. Most terms drop, and we end up with
Similarly, we can plug in and get
Now add them up...
with a sum of