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

✍ Scribed by Paulo Ribenboim; Gary Walsh

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 130 KB
Volume: 74
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1998.2315

No coin nor oath required. For personal study only.

✦ Synopsis

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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