Determine all triplets (a,b,c) of nonzero integers satisfying:
987654321*a + 123456789*b + c = (a + b + c)³

Prove that there are no others.

(In reply to re: A second all-positive solution (spoilers) by Ady TZIDON)

Indeed there is a solution with a+b+c=30000:

27150, 1500, 1350 for a,b and c respectively.

The main run of the program still hasn't gotten up to 30000 yet, but a special run just for this total shows the above result.

 

Posted by Charlie on 2013-06-10 15:28:54