I am confused about a homework problem I have, and don't really know where to begin. The statement is that every negative integer can be written as $2a+3b$ where $a$ and $b$ are either positive or negative integers. I need to prove this. Any idea of where I can start. I am not necessarily looking for a solution, but a place to begin.
Show that every negative integer can be written in the form $2a + 3b$ for some (not necessarily positive) integers $a$ and $b$.