Some Diophantine Equations Related to Positive-rank Elliptic Curves
نویسندگان
چکیده
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 + y + z = a + b + c. These results rely on exhibiting families of positive-rank elliptic curves.
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