Newbie confusion on introduction to proofs.

Question

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?

The existence of such $k$ is what it means for $3$ to be a factor of $2n$. — greelious, Mar 10 '19 at 03:56
If $p$ is divisible by $q$ then, by definition, $\frac{p}{q}=k$ for some $k$ so $p=kq$. — John Douma, Mar 10 '19 at 03:56

score 1 · Answer 1 · answered Mar 10 '19 at 03:56

1

That is a definition:

a is a factor of b if there exists some integer constant k such that $b = ak$.

answered Mar 10 '19 at 03:56

James

3,997

Newbie confusion on introduction to proofs.

1 Answers1