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

Ulf Kühn, Jan Steffen Müller
2015 Functiones et Approximatio Commentarii Mathematici  
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.
doi:10.7169/facm/2015.52.1.10 fatcat:74vjn3oxtfafthodk73rvsoipy