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Original paper

On the Diophantine Equation n(n + d) · · · (n + (k − 1)d) = byl

Volume: 47, Issue: 3, Pages: 373 - 388
Published: Sep 1, 2004
Abstract
We show that the product of four or five consecutive positive terms in arithmetic progression can never be a perfect power whenever the initial term is coprime to the common difference of the arithmetic progression. This is a generalization of the results of Euler and Obláth for the case of squares, and an extension of a theorem of Győry on three terms in arithmetic progressions. Several other results concerning the integral solutions of the...
Paper Details
Title
On the Diophantine Equation n(n + d) · · · (n + (k − 1)d) = byl
Published Date
Sep 1, 2004
Volume
47
Issue
3
Pages
373 - 388
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