## Functiones et Approximatio Commentarii Mathematici

### A height inequality for rational points on elliptic curves implied by the abc-conjecture

#### Abstract

In this short note we show that the uniform $abc$-conjecture puts strong restrictions on the coordinates of rational points on elliptic curves. For the proof we use a variant of Vojta's height inequality formulated by Mochizuki. As an application, we generalize a result of Silverman on elliptic non-Wieferich primes.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 52, Number 1 (2015), 127-132.

Dates
First available in Project Euclid: 20 March 2015

https://projecteuclid.org/euclid.facm/1426857040

Digital Object Identifier
doi:10.7169/facm/2015.52.1.10

Mathematical Reviews number (MathSciNet)
MR3326129

Zentralblatt MATH identifier
06425018

Subjects

#### Citation

Kühn, Ulf; Müller, Jan Steffen. A height inequality for rational points on elliptic curves implied by the abc-conjecture. Funct. Approx. Comment. Math. 52 (2015), no. 1, 127--132. doi:10.7169/facm/2015.52.1.10. https://projecteuclid.org/euclid.facm/1426857040

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