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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

Puni tekst: engleski, pdf (311 KB) str. 279-319 preuzimanja: 207* citiraj
APA 6th Edition
Ziegler, V. (2019). On the existence of S-Diophantine quadruples. Glasnik matematički, 54 (2), 279-319. https://doi.org/10.3336/gm.54.2.03
MLA 8th Edition
Ziegler, Volker. "On the existence of S-Diophantine quadruples." Glasnik matematički, vol. 54, br. 2, 2019, str. 279-319. https://doi.org/10.3336/gm.54.2.03. Citirano 19.10.2021.
Chicago 17th Edition
Ziegler, Volker. "On the existence of S-Diophantine quadruples." Glasnik matematički 54, br. 2 (2019): 279-319. https://doi.org/10.3336/gm.54.2.03
Harvard
Ziegler, V. (2019). 'On the existence of S-Diophantine quadruples', Glasnik matematički, 54(2), str. 279-319. https://doi.org/10.3336/gm.54.2.03
Vancouver
Ziegler V. On the existence of S-Diophantine quadruples. Glasnik matematički [Internet]. 2019 [pristupljeno 19.10.2021.];54(2):279-319. https://doi.org/10.3336/gm.54.2.03
IEEE
V. Ziegler, "On the existence of S-Diophantine quadruples", Glasnik matematički, vol.54, br. 2, str. 279-319, 2019. [Online]. https://doi.org/10.3336/gm.54.2.03

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
https://hrcak.srce.hr/229600

Posjeta: 356 *