%0 Journal Article
%T On the existence of S-Diophantine quadruples
%A Ziegler
%A Volker
%J -
%D 2019
%R 10.3336/gm.54.2.03
%X Sa£żetak Let \(S\) be a set of primes. We call an \(m\)-tuple \((a_1,\ldots,a_m)\) of distinct, positive integers \(S\)-Diophantine, if for all \(i\neq j\) the integers \(s_{i,j}:=a_ia_j+1\) have only prime divisors coming from the set \(S\), i.e. if all \(s_{i,j}\) are \(S\)-units. In this paper, we show that no \(S\)-Diophantine quadruple (i.e.~\(m=4\)) exists if \(S=\{3,q\}\). Furthermore we show that for all pairs of primes \((p,q)\) with \(
%K Diophantine equations
%K S-unit equations
%K Diophantine tuples
%K S-Diophantine quadruples
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=333804