Let $S$ be a positive integer divisible by all the integers $1, 2,...,2015$ and $a_1, a_2,..., a_k$ numbers in $\{1, 2,...,2015\}$ such that $2S \le a_1 + a_2 + ... + a_k$. Prove that we can select from $a_1, a_2,..., a_k$ some numbers so that the sum of these selected numbers is equal to $S$. Lê Anh Vinh