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Wieferich’s criterion and the abc-conjecture. (English) Zbl 0654.10019
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 $\alpha\sp{p-1}\not\equiv 1 (mod p\quad 2)$ where $\alpha$ is a fixed rational number and $\alpha \ne \pm 1,0$, 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 skillfull lemmas.
Reviewer: B.Brindza

11D41Higher degree diophantine equations
14H52Elliptic curves
Full Text: DOI
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