2. Vasya has coins worth 49 tugriks, and Petya has coins worth 99 tugriks (each has a sufficient number of coins). Vasya owes Petya one tugrik. Will they be able to settle the debt?
Solution. We need to find a solution in non-negative integers for the equation $49 n-99 m=1$. Notice that $99-49 \cdot 2=1$ or $49 \cdot(-2)-99 \cdot(-1)=1(*)$. This solution is not suitable for us due to the negativity of the coefficients. Consider the homogeneous equation $49 x-99 y=0$. It has a series of solutions $x=99 k, y=49 k$, where $k$ runs through the set of integers. By adding the solutions of the homogeneous equation to equation (*), we obtain a series of solutions for the non-homogeneous equation, among which we can choose those with positive coefficients, for example, $97 \cdot 49-48 \cdot 99=1$. Answer: they can.

Comment. A correct example is given -7 points.