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 |
Keywords:
quadratic diophantine equations; property of Diophantus; diophantine \(m\)-tuple; diophantine pairOnline Encyclopedia of Integer Sequences:
Numbers k such that k+1 and 3*k+1 are perfect squares.For n > 5, a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3); initial terms are 1, 3, 8, 120, 1680.
