4
$\begingroup$

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 $b$.

  • 0
    did not think to do that. Will try now, thanks. Also thanks for the edit.2012-10-13

1 Answers 1

13

HINT: First find integers $a_0$ and $b_0$ such that $2a_0+3b_0=-1\;.\tag{1}$ Then let $n$ be any positive integer, and see what happens when you multiply equation $(1)$ by $n$.

  • 0
    I entirely agree! Thanks!2012-10-13