Bugi wrote: Determine the biggest possible value of $ m$ for which the equation $ 2005x + 2007y = m$ has unique solution in natural numbers. It is easy to see that $ 2 \cdot 2005 \cdot 2007$ has a unique solution. $ 2005x + 2007y = 2 \cdot 2005 \cdot 2007$ gives $ 2007 \mid x$ and $ 2005 \mid y$. Let $ x = 2005x_1$ and $ y = 2007y_1$ then we have $ x_1+y_1 = 2$, which has the only solution in natural numbers $ x=y=1$. Then assume $ m > 2 \cdot 2005 \cdot 2007$ and it has a unique solution: We easily obtain $ x > 2007$ or $ y > 2005$. (Suppose the contrary: Then $ 2005x + 2007y \le 2 \cdot 2005 \cdot 2007$...) If $ x > 2007$ Then $ x_2 = x - 2007$, $ y_2 = y + 2005$ is also a solution. If $ y > 2005$ Then $ x_2 = x + 2007$, $ y_2 = y - 2005$ is also a solution. So the answer is $ \boxed{2\cdot2005\cdot2007}$