a table having all entries divisible by n
Source: 2009 Grand Duchy of Lithuania, Mathematical Contest p5 (Baltic Way TST)
October 3, 2020
combinatoricstable
Problem Statement
Consider a table whose entries are integers. Adding a same integer to all entries on a same row, or on a same column, is called an operation. It is given that, for infinitely many positive integers , one can obtain, through a finite number of operations, a table having all entries divisible by . Prove that, through a finite number of operations, one can obtain the table whose all entries are zeroes.