Question 2
Let $\alpha,\beta$ be positive real numbers. Emerald makes a trip in the coordinate plane, starting at $(0,0)$. Each minute she moves one unit up or one unit right, always staying in the region $|x-y|\lt 2025$. Upon visiting $(x,y)$, she writes the integer $\lfloor x\alpha+y\beta\rfloor$ there. She writes each nonnegative integer exactly once. Find all pairs $(\alpha,\beta)$ for which such a trip is possible.