15.24. In how many ways can the number $n$ be represented as a sum of several integer terms $a_{i} \geqslant 2$? (Representations differing in the order of the terms are considered different.)
15.24. Answer: $F_{n-1}$. Let the desired number be $x_{n}$. It is clear that $x_{1}=0$, $x_{2}=1$, and $x_{3}=1$. We will prove that $x_{n}=x_{n-1}+x_{n-2}$ for $n \geqslant 3$. The first term can be equal to 2; the number of such representations is $x_{n-2}$. The first term can be greater than 2. Then 1 can be subtracted from it to obtain a representation of the number $n-1$. Therefore, the number of such representations is $x_{n-1}$.