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Cubic Equation (Posted on 2013-06-09) Difficulty: 4 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re(3): A second all-positive solution (spoilers) | Comment 8 of 13 |
(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
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