Question 36
Let $n \gt 1$ be a positive integer and $p$ its greatest prime factor. For each nonempty subset of divisors of the number $n$, write on the board the sum of its elements. Suppose that in this way we have written more than $p$ numbers from the set $\{1, 2, \dots, p+2\}$, and that we have not written any number from this set more than once. Prove that we have not written any number more than once. (Zdeněk Pezlar)