SOLUTION: Xy=2x-y.(x,y are integer)solve for x,y

There are only two solutions (two pairs of solutions) for integer x and y.

They are:

1)  x = 0, y = 0, 

and

2)  x = 1,  y = 1.

There are no other integer solutions.

For the proof, express y via x in the form y =  and note that the right side is less than 2 at x >= 2.