Finding all $S$-Diophantine quadruples for a fixed set of primes $S$

Volker Ziegler

Finding all $S$-Diophantine quadruples for a fixed set of primes $S$

Number Theory 2020-10-23 v1

Authors: Volker Ziegler

Abstract

Given a finite set of primes $S$ and a $m$ -tuple $(a_1,\dots,a_m)$ of positive, distinct integers we call the $m$ -tuple $S$ -Diophantine, if for each $1\leq i < j\leq m$ the quantity $a_ia_j+1$ has prime divisors coming only from the set $S$ . For a given set $S$ we give a practical algorithm to find all $S$ -Diophantine quadruples, provided that $|S|=3$ .

Keywords

S-Diophantine tuples prime set diophantine equations algorithm number theory

Cite

@article{arxiv.2010.11670,
  title  = {Finding all $S$-Diophantine quadruples for a fixed set of primes $S$},
  author = {Volker Ziegler},
  journal= {arXiv preprint arXiv:2010.11670},
  year   = {2020}
}

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