Question 6
Two thieves stole a container of $8$ liters of wine. How can they divide it into two parts of $4$ liters each if all they have is a $3$ liter container and a $5$ liter container? Consider the general case of dividing $m+n$ liters into two equal amounts, given a container of $m$ liters and a container of $n$ liters (where $m$ and $n$ are positive integers). Show that it is possible iff $m+n$ is even and $\frac{m+n}{2}$ is divisible by $\gcd(m, n)$.