Which Prime Numbers Satisfy These Divisibility Conditions?

terafull
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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
 
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I'm seeing this problem asked a lot on the various math forums I frequent. Where does it come from?
 
Which forums (fora) are those, CR?

(See it this way: if you tell me I'll go pester somewhere else.) :P
 
Doesn't looking at the problem just make you instantly think of cubing things?
 
I think I saw the problem, at the least, at
http://www.mymathforum.com/
 

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