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 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 No Rating

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 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        800000000000027150  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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