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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.

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1 Answer 1

up vote 2 down vote accepted

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

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3  
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" –  Danikar 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. –  Danikar Jul 31 '13 at 13:17

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