Open Access
November 2008 A weak effective $abc$-conjecture
Jerzy Browkin
Funct. Approx. Comment. Math. 39(1): 103-111 (November 2008). DOI: 10.7169/facm/1229696557

Abstract

We state an effective version of the $abc$-conjecture, and assuming it we describe all solutions of some diophantine equations. Based on this conjecture we give an effective algorithm for computing an infinite set of primes which are not Wieferich primes.

Citation

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Jerzy Browkin. "A weak effective $abc$-conjecture." Funct. Approx. Comment. Math. 39 (1) 103 - 111, November 2008. https://doi.org/10.7169/facm/1229696557

Information

Published: November 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1241.11033
MathSciNet: MR2043769
Digital Object Identifier: 10.7169/facm/1229696557

Subjects:
Primary: 11D41

Keywords: $abc$-conjecture , equations of Ljunggren-Nagell, Catalan, Fermat, and Brocard-Ramanujan , Wieferich primes

Rights: Copyright © 2008 Adam Mickiewicz University

Vol.39 • No. 1 • November 2008
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