Thread: Math proof help

1. Math proof help

I dont quite know how to attack this.

Here is the problem.

(a divides b) or (a divides c) implies a divides bc.

any help at all would be greatly appreciated

2. Assuming that we are dealing with the integers.
Now, I ask you: if a divides b then does a divide (bc)?

3. Originally Posted by Plato
Assuming that we are dealing with the integers.
Now, I ask you: if a divides b then does a divide (bc)?
I know it does, it is just getting started that is hard. It's obvious that no matter what integer you plug in it divides it, I just don't know how to write it out in proof format. Thanks for your help on this.

4. Originally Posted by padsinseven
I know it does, it is just getting started that is hard. It's obvious that no matter what integer you plug in it divides it, I just don't know how to write it out in proof format. Thanks for your help on this.
If a|b then b = na, where n is an integer. Does this help you?

-Dan

5. Originally Posted by padsinseven
I just don't know how to write it out in proof format.
Your problem is quite simply: WHAT IS A PROOF?
If you do not understand that simple question, see your instructor.
Otherwise, it is pointless to ask for something you do not understand.

6. Originally Posted by Plato
Your problem is quite simply: WHAT IS A PROOF?
If you do not understand that simple question, see your instructor.
Otherwise, it is pointless to ask for something you do not understand.
Thanks for the help Plato. I didn't realize that I was able to assume both a divides b and a divides c. Once I understood that the proof was pretty simple. At least I think that I got it.

7. Originally Posted by padsinseven
Thanks for the help Plato. I didn't realize that I was able to assume both a divides b and a divides c. Once I understood that the proof was pretty simple. At least I think that I got it.
If that is your proof then it isn't correct. You are to assume a|b or a|c, not necessarily both.

I am going to assume that a divides only b. (We can simply switch the roles of b and c if a divides c and not b, so we are losing no generality here by doing this.)

So a|b implies that b = na, where n is some positive integer. Thus
bc = (na)c = (nc)a

But nc is also a positive integer. Thus a|bc as well.

-Dan

8. If a|b the b=an for some n and bc=a(nc), so a|bc.
On the other hand, if a|c the c=am for some m and bc=a(mb), so a|bc.
In either case, a|bc.