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(2): A second all-positive solution (spoilers) by Charlie)

Indeed the initial program has stopped, and the set of all-positive results is complete with these three:

   a     b     c          lhs = rhs    
  450  4500  5050        1000000000000
 7350  6000  6650        8000000000000
27150  1500  1350       27000000000000 

Getting solutions with part positive and part negative values is a separate matter, calling for more analytic insight.

Posted by Charlie on 2013-06-10 21:26:00