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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: 517

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Sažetak

Let S be a set of primes. We call an m-tuple (a1,,am) of distinct, positive integers S-Diophantine, if for all ij the integers si,j:=aiaj+1 have only prime divisors coming from the set S, i.e. if all si,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

Datum izdavanja:

11.12.2019.

Posjeta: 1.259 *

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