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

Katalin Gyarmati

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arXiv · 2604.25017

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

Katalin Gyarmati

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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, $p_1^{k_1}+\dots+p_m^{k_m}=0$ among polynomials.

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Katalin Gyarmati. 2026-04-27. Ramanujan, the taxicab problem for polynomials, and the abc-conjecture. https://arxiv.org/abs/2604.25017

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