A lattice point is a point both of whose coordinates are integers. $$A$$ is $$(0, 0)$$, $$B$$ is $$(4012, 6018)$$. If $$n$$ is the number of lattice points lying on $$\overline{AB}$$, then $$n =$$ _________

The points of $$\overline{AB}$$ are $$(4012t, 6018t)$$ with $$0 \le t \le 1$$. Since $$4012 = 2006 \times 2$$ and $$6018 = 2006 \times 3$$, both coordinates are integers exactly when $$2006t$$ is an integer (their difference $$2006t$$ must be an integer, and conversely). So $$t = \frac{j}{2006}$$ with $$j = 0, 1, \dots, 2006$$, giving $$n = 2007$$ lattice points.