Ramanujan, the taxicab problem for polynomials, and the abc-conjecture
Abstract
Abstract Starting with Ramanujan’s famous taxicab problem, we can study the solvability of the equations $$p^n+q^n=r^n+s^n$$ p n + q n = r n + s n and, more generally, $$p_1^{k_1}+\dots +p_m^{k_m}=0$$ p 1 k 1 + ⋯ + p m k m = 0 among polynomials.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Analytic Number Theory Research
Advanced Mathematical Identities
Publication details
- Journal / source
- Research in Number Theory
- Volume
- 12
- Issue
- 1
- Publication date
- 14 January 2026
- Language
- EN