What does mean this notation $q \mid k$?

Question

Here is two numbers $q$ and $k$. Tell me please what does mean this notation $q \mid k$? Are they relatively prime or something ?

Answer 1

The notation means : $q$ divides $k$ ; There is an integer $m$ with $qm=k$.

Answer 2

It means that $q$ divides $k$, or $k$ is divisible by $q$. Add a little slash and it negates that meaning: $q \nmid k$ means $q$ does not divide $k$.

For example: $3 \mid 1728$, $3 \nmid 1729$.

They are not relatively prime, unless $q = 1$ or $-1$. In fact, if $q \mid k$ then $\gcd(q, k) = |q|$.