Ramanujan, the taxicab problem for polynomials, and the abc-conjecture

Abstract

Starting with Ramanujan's famous taxicab problem, we can study the solvability of the equations $p^n+q^n=r^n+s^n$ and, more generally, $p_1^{k_1}+\cdots +p_m^{k_m}=0$ among polynomials.