Glasnik matematički, Vol. 54 No. 2, 2019.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.54.2.03
On the existence of S-Diophantine quadruples
Volker Ziegler
; Institute of Mathematics, University of Salzburg, Hellbrunnerstrasse 34/I, A-5020 Salzburg, Austria
Sažetak
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 \(p
Ključne riječi
Diophantine equations; S-unit equations; Diophantine tuples; S-Diophantine quadruples
Hrčak ID:
229600
URI
Datum izdavanja:
11.12.2019.
Posjeta: 903 *