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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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