Let N be a positive integer. A "good division of N " is a partition of \{1,2, \ldots, N\} into two disjoint non-empty subsets S_{1} and S_{2} such that the sum of the numbers in S_{1} equals the product of the numbers in S_{2}. For example, if N=5, then
S_{1}=\{3,5\}, \quad S_{2}=\{1,2,4\}
would be a good division.
(a) Find a good division of N=7.
(b) Find an N which admits two distinct good divisions.
(c) Show that if N \geq 5, then a good division exists.