Products of members of Lucas sequences with indices in an interval being a power

In this paper, we show that the product of sufficiently many distinct members of a Lucas sequence with indices in an interval of a fixed length cannot be a perfect power of exponent larger than 1.

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Bibliographic Details
Published in:Journal of number theory 2009-02, Vol.129 (2), p.303-315
Main Authors: Luca, Florian, Shorey, T.N.
Format: Article
Language:English
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Description
Summary:In this paper, we show that the product of sufficiently many distinct members of a Lucas sequence with indices in an interval of a fixed length cannot be a perfect power of exponent larger than 1.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2008.06.015