A note on the number of S -Diophantine quadruples

Florian Luca; Volker Ziegler

Communications in Mathematics (2014)

  • Volume: 22, Issue: 1, page 49-55
  • ISSN: 1804-1388

Abstract

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Let ( a 1 , ⋯ , a m ) be an m -tuple of positive, pairwise distinct integers. If for all 1 ≤ i < j ≤ m the prime divisors of a i a j + 1 come from the same fixed set S , then we call the m -tuple S -Diophantine. In this note we estimate the number of S -Diophantine quadruples in terms of | S | = r .

How to cite

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Luca, Florian, and Ziegler, Volker. "A note on the number of $S$-Diophantine quadruples." Communications in Mathematics 22.1 (2014): 49-55. <http://eudml.org/doc/261965>.

@article{Luca2014,
abstract = {Let $(a_1,\dots , a_m)$ be an $m$-tuple of positive, pairwise distinct integers. If for all $1\le i< j \le m$ the prime divisors of $a_ia_j+1$ come from the same fixed set $S$, then we call the $m$-tuple $S$-Diophantine. In this note we estimate the number of $S$-Diophantine quadruples in terms of $|S|=r$.},
author = {Luca, Florian, Ziegler, Volker},
journal = {Communications in Mathematics},
keywords = {Diophantine equations; $S$-unit equations; $S$-Diophantine tuples; Diophantine equations; -unit equations; -Diophantine tuples},
language = {eng},
number = {1},
pages = {49-55},
publisher = {University of Ostrava},
title = {A note on the number of $S$-Diophantine quadruples},
url = {http://eudml.org/doc/261965},
volume = {22},
year = {2014},
}

TY - JOUR
AU - Luca, Florian
AU - Ziegler, Volker
TI - A note on the number of $S$-Diophantine quadruples
JO - Communications in Mathematics
PY - 2014
PB - University of Ostrava
VL - 22
IS - 1
SP - 49
EP - 55
AB - Let $(a_1,\dots , a_m)$ be an $m$-tuple of positive, pairwise distinct integers. If for all $1\le i< j \le m$ the prime divisors of $a_ia_j+1$ come from the same fixed set $S$, then we call the $m$-tuple $S$-Diophantine. In this note we estimate the number of $S$-Diophantine quadruples in terms of $|S|=r$.
LA - eng
KW - Diophantine equations; $S$-unit equations; $S$-Diophantine tuples; Diophantine equations; -unit equations; -Diophantine tuples
UR - http://eudml.org/doc/261965
ER -

References

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