Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $

Question

I am trying to prove:

$a\mid b \land b\mid c \Rightarrow a\mid c $

$a\mid b$ means that a divides b if there is an integer k, that $b=k\cdot a$

Please give me a hint on how to start, because I have no idea.

score 3 · Accepted Answer · answered Jul 31 '13 at 13:06

3

If $a | b$ and $b | c$, you have $b = ka$ and $c = jb$. Thus $c = (jk)a$. Hence $a | c$.

answered Jul 31 '13 at 13:06

zrbecker

4

That's a bit more than "a hint on how to start", no? – Gerry Myerson Jul 31 '13 at 13:07
Best hint would of been, "think about it", or "use math" – zrbecker Jul 31 '13 at 13:07
3

Maybe. Or maybe one could have written, "You know what $a\mid b$ means; now, what does $b\mid c$ mean? what does $a\mid c$ mean? Can you see some way to put the first two together to get the third?" – Gerry Myerson Jul 31 '13 at 13:12
That is certainly an option. – zrbecker Jul 31 '13 at 13:17

1 Answers1