- #1
mateomy
- 307
- 0
Prove or disprove:
There exists an integer "a" such that [itex]ab\equiv\,0\,(mod 3)[/itex] for every integer "b".
I know I can rewrite the above as [itex]ab=3k[/itex] for some k[itex]\,\in\,\mathbb{Z}[/itex], 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 sort of lost on the wording. Am I on the right path?
Thanks.
There exists an integer "a" such that [itex]ab\equiv\,0\,(mod 3)[/itex] for every integer "b".
I know I can rewrite the above as [itex]ab=3k[/itex] for some k[itex]\,\in\,\mathbb{Z}[/itex], 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 sort of lost on the wording. Am I on the right path?
Thanks.