My problem: Show that if $3$ is a factor of $2n$ then $3$ is also a factor of $n$.
Solution: If $3$ is a factor of $2n$ then some integer constant $k$ exist such that $3k=2n$. Now, $2n$ is even hence $3k$ is even and $k$ is even and so $k$ is divisible by $2$
My question: I don't understand the 'some integer constant exist' part. What does this mean and where does it come from?
That is a definition:
a is a factor of b if there exists some integer constant k such that $b = ak$.