View Single Post
blastoise is offline
Feb13-12, 04:16 PM
P: 22
(1)Assume a, b and n are nonzero integers. Prove that n is divisible by ab if and
only if n is divisible by a and n is divisible by b.

I'm wrong and can't remember why. I spoke to the professor about it for ~ 1 minute so it seems to have slipped my mind, it was because in one case it's true and in the other it isn't here is my proof:

(2)Let a,b and n be non zero integers and assume ab|n. Since ab|n and because a and b must be integers they must both be factors of n. Thus, if a|n or b|n is false then ab will not be a factor of n which means ab∤n.
Thus, ab|n if and only a|n and b|n where a, b and n are non zero integers.

But, then I pulled from a website "[if and only if ]means you must prove that A and B are true and false at the same time. In other words, you must prove "If A then B" and "If not A then not B". Equivalently, you must prove "If A then B" and "If B then A".

I believe that (2) shows if Statement {A} then {B}.
So how would you show if not Statement {a} then not {B}?

I'm going to say
Suppose ab ∤ n is true then a ∤ n and b∤n

Let a = 10, b = 10, n = 10

ab∤ n, but b|n and a|n

The thing I don't understand is how does that disprove (1).

So, the question I'm asking is: Is statement (1) considered true or considered false taken as is. Also, if you could rip my proof apart would be great help(don't hold back criticize away XD )

Phys.Org News Partner Science news on
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes