Sorry, as you will have understood English is not my mother tongue. Especially not for mathematics. And I must admit that restarting to do computations after 33 years does not go very smoothly.
I indeed used "or" where I meant "which can also be written as".
My presentation of the solutions was indeed sloppy, I should have repeated the first set of solutions (any integer x with y=x), plus the solutions of the x^{2}+y^{2}+xy3x3y=0 part.
Finally I mentioned the {0,0} pair since it is not only a solution of the x=y part but also of the x^{2}+y^{2}+xy3x3y=0 part (a double solution?)
