MathDB

In the table are written the positive integers

1, 2,3,...,2018

. John and Mary have the ability to make together the following move: They select two of the written numbers in the table, let

a,b

and they replace them with the numbers

5a-2b

and

3a-4b

. John claims that after a finite number of such moves, it is possible to triple all the numbers in the table, e.g. have the numbers:

3, 6, 9,...,6054

. Mary thinks a while and replies that this is not possible. Who of them is right?

Problem Statement