On the existence of S-Diophantine quadruples
Let S be a set of primes. We call an m-tuple (a1,… ,am) of distinct, positive integers S-Diophantine, if for all i≠ j 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=...
| Permalink: | http://skupni.nsk.hr/Record/nsk.NSK01001075553/Details |
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| Matična publikacija: |
Glasnik matematički (Online) 54 (2019), 2 ; str. 279-319 |
| Glavni autor: | Ziegler, Volker (Author) |
| Vrsta građe: | e-članak |
| Jezik: | eng |
| Predmet: | |
| Online pristup: |
https://doi.org/10.3336/gm.54.2.03 Glasnik matematički (Online) Hrčak |
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| 008 | 200928s2019 ci d |o |0|| ||eng | ||
| 024 | 7 | |2 doi |a 10.3336/gm.54.2.03 | |
| 035 | |a (HR-ZaNSK)001075553 | ||
| 040 | |a HR-ZaNSK |b hrv |c HR-ZaNSK |e ppiak | ||
| 041 | 0 | |a eng |b eng | |
| 042 | |a croatica | ||
| 044 | |a ci |c hr | ||
| 080 | 1 | |a 51 |2 2011 | |
| 100 | 1 | |a Ziegler, Volker |4 aut | |
| 245 | 1 | 0 | |a On the existence of S-Diophantine quadruples |h [Elektronička građa] / |c Volker Ziegler. |
| 300 | |b Graf. prikazi. | ||
| 504 | |a Bibliografija: 21 jed. | ||
| 504 | |a Abstract. | ||
| 520 | |a Let S be a set of primes. We call an m-tuple (a1,… ,am) of distinct, positive integers S-Diophantine, if for all i≠ j 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 <q and p ≡ 3 mod 4 no {p,q}-Diophantine quadruples exist, provided that (p,q) is not a Wieferich prime pair. | ||
| 653 | 0 | |a Diofantske jednadžbe |a Diofantove četvorke | |
| 773 | 0 | |t Glasnik matematički (Online) |x 1846-7989 |g 54 (2019), 2 ; str. 279-319 |w nsk.(HR-ZaNSK)000659858 | |
| 981 | |b Be2019 |b B05/19 | ||
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