Wieferich's criterion and the abc-conjecture
type: Item
instance of: scholarly article
title: Wieferich's criterion and the abc-conjecture
zbMATH Open document ID: 0654.10019
DOI: 10.1016/0022-314X(88)90019-4
author: Joseph H. Silverman
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: The following result is proved. The so called ``abc-conjecture'' of Masser and Oesterlé implies that the number of primes less than \(X\) for which \(\alpha^{p-1}\not\equiv 1 \pmod{p^2}\) where \(\alpha\) is a fixed rational number and \(\alpha \neq \pm 1,0\), is at least \(O(\log X)\). An analogous result is also proved for points of infinite order on elliptic curves having certain \(j\)-invariants. The proofs base on several skillful lemmas.
reviewed by: Bela Brindza
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 4067006
zbMATH Keywords: Wieferich's criterion
zbMATH Keywords: first case of Fermat's last theorem
zbMATH Keywords: abc- conjecture
zbMATH Keywords: points of infinite order
zbMATH Keywords: elliptic curves
zbMATH Keywords: j-invariants
MaRDI profile type: Publication
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Wikidata QID: Q55892244
description: scientific article; zbMATH DE number 4067006