On the $abc$ and the $abcd$ conjectures
Number Theory
2024-06-10 v1
Abstract
We revisit a subexponential bound for the conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the -terms conjecture under a suitable hypothesis on the size of the variables.
Cite
@article{arxiv.2406.05083,
title = {On the $abc$ and the $abcd$ conjectures},
author = {Hector Pasten and Rocío Sepúlveda-Manzo},
journal= {arXiv preprint arXiv:2406.05083},
year = {2024}
}