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The ABC Conjecture and the Powerful Part of Terms in Binary Recurring Sequences

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
74
Issue
1
Identifiers
DOI: 10.1006/jnth.1998.2315

Abstract

Abstract We consider non-degenerate binary recurring sequences with positive discriminant, relatively prime parameters, and whose initial terms satisfy a certain divisibility condition. Assuming that the ABC conjecture is true, we show that the powerful part of the terms of the sequence remain “small.” In particular, such sequences have only finitely many terms which are powerful numbers.

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