The ABC conjecture and the powerful part of terms in binary recurring sequences

DOI10.1006/jnth.1998.2315zbMath0923.11033OpenAlexW2048054919WikidataQ122958990 ScholiaQ122958990MaRDI QIDQ1284204

Paulo Ribenboim, Peter Gareth Walsh

Publication date: 30 March 1999

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1998.2315

zbMATH Keywords

ABC conjecturepowerful numbersbinary recurrence sequence

Mathematics Subject Classification ID

Higher degree equations; Fermat's equation (11D41) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items

A new approach to polynomial identities, The \(abc\) conjecture and the fundamental system of units of certain real bicyclic biquadratic fields., Weak and strong orders of linear recurring sequences, ABC implies there are infinitely many non-Fibonacci-Wieferich primes, Linear recurrence sequences without zeros

Cites Work

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• Wieferich's criterion and the abc-conjecture
• Perfect powers in second order linear recurrences
• The \(abc\) conjecture
• Old and new conjectured diophantine inequalities
• On the Diophantine equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences.
• Some Remarks on the abc-Conjecture