How can I now solve $x^2+y^2=x+y+2$?
I could not do anything because $$x^2-x+y^2-y=2\Rightarrow x(x-1)+y(y-1)=2$$ And that is where I am stuck!!
2026-03-26 06:26:40.1774506400
Diophantine trouble
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Hint. Your equation is equivalent to $$(2x-1)^2+(2y-1)^2=10$$ where $10=(\pm 1)^2+(\pm 3)^2$.