English

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

Number Theory 2026-04-29 v1

Abstract

Starting with Ramanujan's famous taxicab problem, we can study the solvability of the equations pn+qn=rn+snp^n+q^n=r^n+s^n and, more generally, p1k1++pmkm=0p_1^{k_1}+\dots+p_m^{k_m}=0 among polynomials.

Keywords

Cite

@article{arxiv.2604.25017,
  title  = {Ramanujan, the taxicab problem for polynomials, and the abc-conjecture},
  author = {Katalin Gyarmati},
  journal= {arXiv preprint arXiv:2604.25017},
  year   = {2026}
}
R2 v1 2026-07-01T12:38:10.568Z