Let $M$ be the set of positive odd integers. For every positive integer $n$, denote $A(n)$ the number of the subsets of $M$ whose sum of elements equals $n$. For instance, $A(9) = 2$, because there are exactly two subsets of $M$ with the sum of their elements equal to $9$: $\{9\}$ and $\{1, 3, 5\}$. a) Prove that $A(n) \le A(n + 1)$ for every integer $n \ge 2$. b) Find all the integers $n \ge 2$ such that $A(n) = A(n + 1)$