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The Product of Like-Indexed Terms in Binary Recurrences

✍ Scribed by F. Luca; P.G. Walsh

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
188 KB
Volume
96
Category
Article
ISSN
0022-314X

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✦ Synopsis

In recent work by Hajdu and Szalay, Diophantine equations of the form Γ°a k Γ€ 1Þðb k Γ€ 1Þ ΒΌ x 2 were completely solved for a few pairs Γ°a; bÞ: In this paper, a general finiteness theorem for equations of the form u k v k ΒΌ x n is proved, where u k and v k are terms in certain types of binary recurrence sequences. Also, a unified computational approach for solving equations of the type Γ°a k Γ€ 1Þðb k Γ€ 1Þ ΒΌ x 2 is described, and this approach is used to completely solve such equations for almost all Γ°a; bÞ in the range 1oaob4100: In the final section of this paper, it is shown that the abc conjecture implies much stronger results on these types of Diophantine problems.

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