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

Florian Luca; Volker Ziegler

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

Number Theory 2014-03-25 v2

Authors: Florian Luca , Volker Ziegler

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 $|S|=r$ .

Keywords

S-Diophantine tuples Diophantine quadruples prime divisors number theory multiplicative structure

Cite

@article{arxiv.1403.1674,
  title  = {A note on the number of $S$-Diophantine quadruples},
  author = {Florian Luca and Volker Ziegler},
  journal= {arXiv preprint arXiv:1403.1674},
  year   = {2014}
}

Comments

Correction of some typos and an error in Corollary 1

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

Abstract

Keywords

Cite

Comments

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