A generalization of a theorem of Baker and Davenport. (English) Zbl 0911.11018

Dujella, Andrej; Pethő, Attila

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)

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