Determine all possible triplets (A,B,C) of positive integers with A ≤ B ≤ C that satisfy this system of equations:
A = P(B)+ P(C), B = P(A) + P(C), and C = P(A) + P(B)
Prove that there are no others.
No Solution Yet  Submitted by K Sengupta 
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re(2): results so far, but no proof in sight 

(In reply to re: results so far, but no proof in sight by Charlie)
For my intuition it is enough, for a finicky purist NO...
I wonder, what proof will be presented in the "official" solution.
Posted by Ady TZIDON on 20130805 11:09:33 