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

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
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