Rad HAZU, Matematičke znanosti, Vol. 18 (2014), 7-13.


Ljubica Baćić and Alan Filipin

Primary School Nikola Andrić, 32000 Vukovar, Croatia
e-mail: ljubica.bacic@skole.hr

Faculty of Civil Engineering, University of Zagreb, 10000 Zagreb, Croatia
e-mail: filipin@master.grad.hr

Abstract.   In this paper we will significantly improve the known bound on the number of D(4)-quintuples, illustrating the elegant use of the results the authors proved in [1] together with more efficient way of counting the number of m-tuples that was introduced in [5]. More precisely, we prove that there are at most 7 · 1036 D(4)-quintuples.

2010 Mathematics Subject Classification.   11D09, 11J68.

Key words and phrases.   Diophantine tuples, simultaneous Diophantine equations.

Full text (PDF) (free access)


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