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arXiv · 1304.1442

Some Diophantine equations related to positive-rank elliptic curves

Gwyneth Moreland·Michael E. Zieve
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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.

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Gwyneth Moreland, Michael E. Zieve. 2013-04-04. Some Diophantine equations related to positive-rank elliptic curves. https://arxiv.org/abs/1304.1442

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