Question 142
A positive integer $N$ is called stable if it is possible to split the set of all positive divisors of $N$ (including $1$ and $N$) into two subsets that have no elements in common, which have the same sum. For example, $6$ is stable, because $1+2+3=6$ but $10$ is not stable. Is $2^{2008} \cdot 2008$ stable?