(In reply to
re: Possible solution by Jer)
this is an elliptic curve and a known property of elliptic curves is that the set of integer points is finite. Using the following two lines in Maga
E:=EllipticCurve([0,0,0,1,1]);
IntegralPoints(E);
you can see that these 3 points are the only ones with positive cooridnates. This can be ran for free at the following link
http://magma.maths.usyd.edu.au/calc/

Posted by Daniel
on 20160516 09:13:02 