for all integers a,b,and c if a|bc then a|b or a|c

Sep 2013
567
27
Portland
for all integers a,b,and c if a|bc then a|b or a|c

let a,b, and c be integers such that a|bc

then,

ak=b or ak=c (is this using what I need to prove to prove it??)

this doesn't seem right
 

Prove It

MHF Helper
Aug 2008
12,897
5,001
This is false, consider b = 6 and c = 4. Their product bc = 24. But if a = 8, then a|bc, but a does not divide either b or c.
 
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Sep 2013
567
27
Portland
oh, thanks I was doing some examples but I was always doing a <b and a<c
 

Prove It

MHF Helper
Aug 2008
12,897
5,001
Well it may be true for all a<b and a<c though. Will have a think about it...
 
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Dec 2012
1,145
502
Athens, OH, USA
Of course it's still false. Example a=6, b=8 and c=9; 6 divides 72 but 6 divides neither 8 nor 9.
 
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