Definition of a Field of Characteristic $n$?

Definition of a Field of Characteristic $n$?

Let $V$ be a vector space over a field of characteristic not equal to $2$.
Prove that $\{u, v\}$ is linearly independent with $u, v$ being distinct
if and only if $\{u+v, v-v\}$ is linearly independent.

Perhaps the text was meant for someone at a higher level. I never learned
what a field of characteristic $n$ means. After googling for a while, I am
still stuck. From various sources, it seems that the characteristic of $n$
is referring to the modulus $n$. If my understanding is correct, when the
question say that $\{u, v\}$ is linearly independent, $0 = au + bv$, does
$a,b$ equal $0$ or $0$ mod($n$)?

I tested this question many times. If $a, b = 0$, the condition of having
a field of characteristic not equal to $2$ is trivial. On the other hand,
if $a, b \equiv 0$ mod($n$), then the statement in the question is
actually false. May someone kindly point me in the right direction?
Thanks!