Some Diophantine equations related to positive-rank elliptic curves
Number Theory
2013-04-05 v1
Abstract
We give conditions on the rational numbers a,b,c which imply that there are infinitely many triples (x,y,z) of rational numbers such that x+y+z=a+b+c and xyz=abc. We do the same for the equations x+y+z=a+b+c and x^3+y^3+z^3=a^3+b^3+c^3. These results rely on exhibiting families of positive-rank elliptic curves.
Cite
@article{arxiv.1304.1442,
title = {Some Diophantine equations related to positive-rank elliptic curves},
author = {Gwyneth Moreland and Michael E. Zieve},
journal= {arXiv preprint arXiv:1304.1442},
year = {2013}
}
Comments
12 pages