Split Into Groups With Different Remainders of Sums
Source: Ukrainian Mathematical Olympiad 2023. Day 2, Problem 8.8
April 5, 2023
number theory
Problem Statement
You are given a set of integers, all of which give distinct remainders modulo some integer . Show that for any integer you can split this set into nonempty groups so that the sums of elements in these groups are distinct modulo .Proposed by Anton Trygub