Can zigzag carbon nanotubes be expressed as a mathematical vector?

[tomwilliam]

Homework Statement

I'm trying to express the conditions for a zigzag carbon nanotube in a mathematical vector.

Homework Equations

B = na₁ + ma₂

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.
Thanks in advance
P.S B, a1 and a2 are vectors, but I couldn't find the bold button.

 

[TeethWhitener]

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.