Question 40
Let $s, t$ be given nonzero integers, and let $(x, y)$ be any ordered pair of integers. A move changes $(x, y)$ to $(x + t, y - s)$. The pair $(x, y)$ is 'good' if after some (maybe zero) number of moves it describes a pair of integers that are not relatively prime.
a. Determine if $(s, t)$ is a good pair.
b. Show that for any $s$ and $t$ there is a pair $(x, y)$ which is not good.
a. Determine if $(s, t)$ is a good pair.
b. Show that for any $s$ and $t$ there is a pair $(x, y)$ which is not good.