MathDB
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 0,1,2,3,40, 1, 2, 3, 4, he can repeat numbers. Nicolas can realize the following operation: change one number of the board, by the remainder(in the division by 55) 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.