definitions

• Feb 7th 2010, 08:11 AM
alexandrabel90
definitions
why is it not true for all positive intergers a,b,c that if ab l c then a l c ?
• Feb 7th 2010, 08:24 AM
Swlabr
Quote:

Originally Posted by alexandrabel90
why is it not true for all positive intergers a,b,c that if ab l c then a l c ?

$(ab)k=c \Rightarrow a(bk) = c \Rightarrow a|c$.

Why do you think this is false?
• Feb 7th 2010, 08:47 AM
HallsofIvy
Quote:

Originally Posted by alexandrabel90
why is it not true for all positive intergers a,b,c that if ab l c then a l c ?

No one can answer that because it is true that if ab divides c, the a divides c (and, of course, so does b). You may be thinking of the other way around. if c|ab, then it not necessarily true that c|a or c|b. For example, if c= 4, a= 2, b= 6, 4 divides ab= 12 but does not divide either 2 or 6. 4= 2(2)contains a factor from 2 and from 6.
• Feb 7th 2010, 08:52 AM
alexandrabel90
i thought it was true too...but in a maths question that i was given:

is the following true for all positive intergers a, b ,c?
(a) a l bc and b is not divisible by a then a l c
(b) if ab + 1 = c^2 then a and c are coprime
(c) if ab l c then a l c

im sure that (a) is true..so i thought that means (b) and (c) are false...is there a mistake in the answer? both (a) and (c) are true right?
• Feb 7th 2010, 08:57 AM
Swlabr
Quote:

Originally Posted by alexandrabel90
i thought it was true too...but in a maths question that i was given:

is the following true for all positive intergers a, b ,c?
(a) a l bc and b is not divisible by a then a l c
(b) if ab + 1 = c^2 then a and c are coprime
(c) if ab l c then a l c

im sure that (a) is true..so i thought that means (b) and (c) are false...is there a mistake in the answer? both (a) and (c) are true right?

The question is asking you to verify if each of the propositions are correct or not. It is, I suppose, badly worded, but essentially you have to answer the three parts individually.

I suspect the "Is" should be an "Are", although my grammar isn't very good...