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arXiv · 1403.1674

A note on the number of $S$-Diophantine quadruples

Florian Luca·Volker Ziegler
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Abstract

Let $(a_1,\dots, a_m)$ be an $m$-tuple of positive, pairwise distinct, integers. If for all $1\leq i< j \leq m$ the prime divisors of $a_ia_j+1$ come from the same fixed set $S$, then we call the $m$-tuple $S$-Diophantine. In this note we estimate the number of $S$-Diophantine quadruples in terms of $|S|=r$.

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Florian Luca, Volker Ziegler. 2014-03-07. A note on the number of $S$-Diophantine quadruples. https://arxiv.org/abs/1403.1674

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