Question 24
The positive integers $1, 2, 3, \ldots, 2018$ are written on a board. John and Mary may make the following move:
they select two of the numbers written on the board, say $\alpha, \beta$, and replace them with the numbers $5\alpha - 2\beta$ and $3\alpha - 4\beta$.
John asserts that after a finite number of such moves it is possible to have on the board the numbers $3, 6, 9, \ldots, 6054$. Mary answers that this is not possible. Who is right?
they select two of the numbers written on the board, say $\alpha, \beta$, and replace them with the numbers $5\alpha - 2\beta$ and $3\alpha - 4\beta$.
John asserts that after a finite number of such moves it is possible to have on the board the numbers $3, 6, 9, \ldots, 6054$. Mary answers that this is not possible. Who is right?