MathDB

4

Part of 2019 Greece Junior Math Olympiad

Problems(1)

Combinatorics

Source: Greece Archimedes Junior 2019

3/16/2020
In the table are written the positive integers 1,2,3,...,20181, 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,ba,b and they replace them with the numbers 5a−2b5a-2b and 3a−4b3a-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,...,60543, 6, 9,...,6054. Mary thinks a while and replies that this is not possible. Who of them is right?
combinatorics