MathNet 2025-part-02 — 186 problems (EN–VI) Question 80

Let $n$ be a positive integer and $A = \{n, n+1, \dots, 2n-1\}$. Prove that there is a number $a \in A$ such that the sum of elements of the set $A \setminus \{a\}$ is not divisible by any element of $A$.