Zigzag carbon nanotubes

1. Sep 18, 2011

tomwilliam

1. The problem statement, all variables and given/known data
I'm trying to express the conditions for a zigzag carbon nanotube in a mathematical vector.

2. Relevant equations

B = na1 + ma2

3. The attempt at a solution

I want to say "either a=0 or b=0", but must I also say that it can't be a=b=0 or is that already excluded in the statement? I'm not sure of the mathematical logic at work.
You could say "either $n=0$ or $m=0$ but not both." Alternatively, since $\mathbf{a}_1$ and $\mathbf{a}_2$ are identical graphene unit cell vectors, they're interchangeable, so you could just say "$n=0$ and $m \neq 0$," which is equivalent to the first statement.