Some Diophantine equations related to positive-rank elliptic curves
Moreland, Gwyneth · Zieve, Michael E.
Original · EN
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 x³+y³+z³=a³+b³+c³. These results rely on exhibiting families of positive-rank elliptic curves.
English translation
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