perplexus.info :: Just Math : Cubic Equation

Cubic Equation (Posted on 2013-06-09)

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 |

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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