# Proof Question

1. Jun 8, 2012

### mateomy

Prove or disprove:

There exists an integer "a" such that $ab\equiv\,0\,(mod 3)$ for every integer "b".

I know I can rewrite the above as $ab=3k$ for some k$\,\in\,\mathbb{Z}$, but other than that I'm not sure where to go. I realize that dividing any of the above will not necessarily result in an integer which contradicts the initial statement, but I'm sorta lost on the wording. Am I on the right path?

Thanks.

2. Jun 8, 2012

### scurty

Try dividing both sides by 3 (so the right side is an integer). Do you see an obvious choice for a so that the left side is an integer or are there no choices?

3. Jun 8, 2012

### mateomy

As long as a is a multiple of 3 it would work. I just don't know how to word that correctly.

4. Jun 8, 2012

### algebrat

Here's how you might start the proof:

Indeed, let a=3, then for any b...