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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 Another solution (spoiler) | Comment 2 of 13 |
Charlie's done all the hard work.

Clearly, another solution is (a,b,c) = (-450,-4500,-5050)

We might be able to prove that these are unique by letting 
  a = 450 + X
  b = 4500 + y
  c = 5050 + z
but the math still looks difficult

Or maybe doing something mod 450 would work ...

  Posted by Steve Herman on 2013-06-09 19:46:22
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