Remainder and divison
Source: May Olympiad(Olimpiada de Mayo) 2005
February 21, 2018
combinatoricsnumber theory
Problem Statement
Gonçalo writes in a board four of the the following numbers , he can repeat numbers. Nicolas can realize the following operation: change one number of the board, by the remainder(in the division by ) of the product of others two numbers of the board. Nicolas wins if all the four numbers are equal, determine if Gonçalo can choose numbers such that Nicolas will never win.