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arXiv · 2406.05083

On the $abc$ and the $abcd$ conjectures

Hector Pasten·Rocío Sepúlveda-Manzo
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Abstract

We revisit a subexponential bound for the $abc$ 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 $4$-terms $abc$ conjecture under a suitable hypothesis on the size of the variables.

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Hector Pasten, Rocío Sepúlveda-Manzo. 2024-06-07. On the $abc$ and the $abcd$ conjectures. https://arxiv.org/abs/2406.05083

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