Acta Mathematica Hungarica

, Volume 159, Issue 2, pp 589–602 | Cite as

Diophantine \(\mathcal{S} \)-quadruples with two primes which are twin



We show that there are only finitely many pairs of twin primes \((p, p+2) \) such that there exists an\(\mathcal{S} \)-Diophantine quadruple in the sense of Szalay and Ziegler for the set\(\mathcal{S} \) of integers composed only of primes p and p + 2.

Key words and phrases

Diophantine equation linear form in logarithms 

Mathematics Subject Classification



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The author thanks the referee for helpful comments and for detecting a numerical error in a previous version of the manuscript. This paper was written during the 2nd International Conference on Diophantine m-tuples and related topics held at Purdue University North-West in October, 2018. The author thanks the organisers for the invitation and support.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.School of MathematicsUniversity of the WitwatersrandWitwatersrandSouth Africa
  2. 2.King Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of MathematicsUniversity of OstravaOstrava 1Czech Republic

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