Subsets of a set form a complete residue system mod 2^n
Source: Mongolia national olympiad 2024
April 10, 2024
combinatoricsnumber theorycomplete residue system
Problem Statement
A set consisting of positive integers is called if the following condition holds:
For any two different subsets of , say and , the number is not divisible by .
(Here, for a set , denotes the sum of the elements of )
Given , find the number of good sets of size , all of whose elements is strictly less than .