Question 158
Prove that every positive integer $n$, except a finite number of them, can be represented as a sum of $2004$ positive integers: $n = a_1 + a_2 + \dots + a_{2004}$, where $1 \le a_1 \lt a_2 \lt \dots \lt a_{2004}$, and $a_i \mid a_{i+1}$, $i = 1, 2, \dots, 2003$. (posed by Chen Yonggao)