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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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re(3): an open letter to Charlie | Comment 12 of 13 |
(In reply to re(2): an open letter to Charlie by Charlie)

Charlie:


I guess that my substitution, x = a + b + c would speed things up. 

This leads to:

987654320*a + 123456788*b = x^3 - x

And now the equation is linear for any given x.

  Posted by Steve Herman on 2013-06-13 00:27:29
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