Which Prime Numbers Satisfy These Divisibility Conditions?

[terafull]

Find all prime numbers $$(p,q,r)$$, that numbers $$pq+pr+rq$$ and $$p^3+q^3+r^3-2pqr$$ are divided by $$p+q+r$$

 

[CRGreathouse]

I'm seeing this problem asked a lot on the various math forums I frequent. Where does it come from?

 

[dodo]

Which forums (fora) are those, CR?

(See it this way: if you tell me I'll go pester somewhere else.) :P

 

[matt grime]

Doesn't looking at the problem just make you instantly think of cubing things?

 

[CRGreathouse]

I think I saw the problem, at the least, at
http://www.mymathforum.com/