Prove that if |, then |, for any , , , ∈ ℕ

Question

So I have, if abc|cd, then abc(k) = cd. I'm very confused on how to continue

Try to manipulate the equation so it is in the form $ab (m) = bcd$. — player3236, Oct 21 '20 at 14:30
@EwanDelanoy Never introduce division in an elementary number theory question about divisibility. Factoring is fine. Dividing is not. This is generally taught before division is formally introduced. — JMoravitz, Oct 21 '20 at 14:33

score 3 · Answer 1 · answered Oct 21 '20 at 14:35

3

Hint:

Since $abc\mid cd$ we know that there is some integer $k$ such that $abck = cd$

If we were to multiply both sides by $b$...

Then $ab(bck)=bcd$ and noting that $bck$ is an integer...

answered Oct 21 '20 at 14:35

JMoravitz

1 Answers1