The ABC conjecture and the powerful part of terms in binary recurring sequences
type: Item
instance of: scholarly article
title: The ABC conjecture and the powerful part of terms in binary recurring sequences
zbMATH Open document ID: 0923.11033
author: Paulo Ribenboim
author: P. G. Walsh
published in: Journal of Number Theory
publication date: 1999-03-30T00:00:00Z
review text: Binary recurrence sequences have many interesting arithmetic properties like identities and divisibility properties. Under a certain assumption -- the so-called ABC conjecture is true -- such sequences with a positive discriminant have only finitely many terms which are powerful numbers. Here a natural number \(n\) is powerful if \(p^2\) divides \(n\) whenever a prime \(p\) divides \(n\).
reviewed by: Gerhard Rosenberger
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11D41
zbMATH DE Number: 1271770
zbMATH Keywords: binary recurrence sequence
zbMATH Keywords: ABC conjecture
zbMATH Keywords: powerful numbers
MaRDI profile type: Publication
full work available at URL: jnth.1998.2315
OpenAlex ID: W2048054919
Wikidata QID: Q122958990
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DOI: 10.1006/JNTH.1998.2315
description: scientific article; zbMATH DE number 1271770