Let $n$ be a positive integer. What is the smallest value of $m$ with $m > n$ such that the set $M = \{n, n + 1, ..., m\}$ can be partitioned into subsets so that in each subset, there is a number which equals to the sum of all other numbers of this subset?
Problem
Source: 2021 Saudi Arabia Training Lists p31 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests
Tags: set, partition, Subsets, combinatorics