Discrete math (don't know how to start)

Maybe, maybe not. What does it tell you?

 

That looks correct. Is it useful?

 

You don't know how to find all of the solutions to a x b = 2352?

 

Ah. So you do know how to solve the problem, you're just fishing for other methods.

This particular method could be streamlined a bit, because it's easy enough to limit yourself to writing down just those pairs with, for example, a dividing lcm(a,b). There are probably other constraints you could easily impose at the same time.

 

BTW, a different method would be to look at prime factorizations.

But in the end, I think that after optimization, both methods would lead to the same algorithm.

 

Er, what is there to explain? You know how to find all the solutions to a x b = 2352, so now we're just imposing some of the information from the original problem to streamline our work.

I thought that's what I was doing....

 

It's late for me, so I'll just leave you with two more comments.


(1) There's no shame in having an inelegant solution!

If you have a line of thought that looks like it will work, then it's worth pursuing. I'm fairly good at solving hard problems, and one of the reasons is that if I see a path that I can make progress upon, then I go down that path, even if it appears long and tedious. Quite often, I can finish that long and tedious path in much less time than it would take to come up with the clever, "quick" proof.

And that said, once you take a path and have worked stuff out... you can learn from it and use that experience to continue attacking the problem.


(2) Divisibility is very, very important in number theory.

This is something you should take the time to understand thoroughly -- you should be able to answer questions like "find all numbers x such that 12 divides x and x divides 2160" just as easily as you can answer questions like "find all factors of 504".

 

Hrm. I expected three answers. (But I could be wrong)