(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let n be a positive integer and let D(n) be the set of all positive integers d such that d divides n. For example, D(10)={1,2,5,10}. It's easily shown that the divides relation (xRy if x divides y) is a partial ordering on D(n), but for what n is the D(n) totally ordered?

2. Relevant equations

3. The attempt at a solution

I've already verified that for all n, D(n) is a partial ordering. I've also made the observation that, for all n=2^s + 3^t where s,t are natural numbers D(n) is totally ordered. However, I'm having a difficult time proving this. For nonzero s and t, n is prime and D(n) is clearly totally ordered. For the cases where s=0 or t=0, it's more difficult to prove. Any suggestions? Is this the right way to go about this?

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# Homework Help: Proving Total Order

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