Dujella, Andrej; Pethő, Attila A generalization of a theorem of Baker and Davenport. (English) Zbl 0911.11018 Q. J. Math., Oxf. II. Ser. 49, No. 195, 291-306 (1998). A set of positive integers \(\{a_1,a_2,\dots, a_m\}\) is said to have the property of Diophantus if \(a_ia_j+1\) is a perfect square for all \(1\leq i<j\leq m\) and is called a diophantine \(m\)-tuple. Main results are: The diophantine pair \(\{1,3\}\) can be extended to infinitely many diophantine 4-tuples; cannot be extended to a diophantine 5-tuple. Reviewer: E.L.Cohen (Ottawa) Cited in 5 ReviewsCited in 148 Documents MSC: 11D09 Quadratic and bilinear Diophantine equations 11J86 Linear forms in logarithms; Baker’s method Keywords:quadratic diophantine equations; property of Diophantus; diophantine \(m\)-tuple; diophantine pair PDF BibTeX XML Cite \textit{A. Dujella} and \textit{A. Pethő}, Q. J. Math., Oxf. II. Ser. 49, No. 195, 291--306 (1998; Zbl 0911.11018) Full Text: DOI OpenURL