Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0654.10019
Silverman, Joseph H.
Wieferich's criterion and the abc-conjecture. (English)
[J] J. Number Theory 30, No.2, 226-237 (1988). ISSN 0022-314X; ISSN 1096-1658/e

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.
[B.Brindza]

MSC 2000:: *11D41 Higher degree diophantine equations
14H52 Elliptic curves

Keywords: Wieferich's criterion; first case of Fermat's last theorem; abc- conjecture; points of infinite order; elliptic curves; j-invariants

Cited in: Zbl 1241.11037 Zbl 1158.14029 Zbl 1144.11046 Zbl 1135.11332 Zbl 0988.11004 Zbl 0964.11026 Zbl 0905.11002

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]