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PRODUCTS OF CONSECUTIVE INTEGERS

Published online by Cambridge University Press:  24 August 2004

MICHAEL A. BENNETT
MICHAEL A. BENNETT
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Z2 Canadabennett@math.ubc.ca
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Abstract

In this paper, a number of results are deduced on the arithmetic structure of products of integers in short intervals. By way of an example, work of Saradha and Hanrot, and of Saradha and Shorey, is completed by the provision of an answer to the question of when the product of $k$ out of $k+1$ consecutive positive integers can be an ‘almost’ perfect power. The main new ingredient in these proofs is what might be termed a practical method for resolving high-degree binomial Thue equations of the form $ax^n - by^n = \pm 1$, based upon results from the theory of Galois representations and modular forms.

Keywords

11D4111D61
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 5 , September 2004 , pp. 683 - 694
Copyright
© The London Mathematical Society 2004

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