100n coins to be shared by n thieves
Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 2013 p2
February 17, 2020
combinatorics
Problem Statement
Each of the thieves in the -member party () charged a certain number of coins. All the coins were . Thieves decided to share their prey as follows: at each step, one of the bandits puts one coin to the other two. Find them all natural numbers for which after a finite number of steps each outlaw can have coins no matter how many coins each thug has charged.