Thread: Running Through Positive Divisors

Hi there! This is my first post!

I am confused over what is means to run through the divisors. The question is:

Show that if n>0, then as d runs through the positive divisors of n, so does n/d.

Thanks for your help!

Originally Posted by KatyCar

Hi there! This is my first post!

I am confused over what is means to run through the divisors. The question is:

Show that if n>0, then as d runs through the positive divisors of n, so does n/d.

Thanks for your help!

What does "run through" mean?

It's an expression used in many number theory texts, which essentially means : "as takes on all possible values of divisors of , so does ".

Originally Posted by Bruno J.

It's an expression used in many number theory texts, which essentially means : "as takes on all possible values of divisors of , so does ".

Isn't the question fairly trivial then...

The question most likely has a very simple solution

Unfortunately I am not familiar with number theory as I have just decided to start studying it so I do not see the solution.

If someone wouldn't mind giving a little more of an explanation it would me most helpful. Thanks!

Well consider the set of all pairs where is a divisor of . What you want to show is that every divisor occurs not only as a first element of some pair (which it does by definition) but also as the second element of some pair. Hint : show that when is a divisor of , is also a divisor of . Which pair has as a first element?