MathDB

5

Part of 2009 Grand Duchy of Lithuania

Problems(1)

a table having all entries divisible by n

Source: 2009 Grand Duchy of Lithuania, Mathematical Contest p5 (Baltic Way TST)

10/3/2020
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 nn, one can obtain, through a finite number of operations, a table having all entries divisible by nn. Prove that, through a finite number of operations, one can obtain the table whose all entries are zeroes.
combinatoricstable