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Imperfectly Cubed (Posted on 2013-09-29) Difficulty: 3 of 5
Consider three distinct odd positive integers A, B and C - none of which is a perfect cube.

Can the respective cube roots of A, B and C form three consecutive terms of an arithmetic sequence?

If so, provide an example. If not, prove it.

No Solution Yet Submitted by K Sengupta    
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Solution solution-an example | Comment 1 of 6
Will provide an example:

TAKE  n such that n^3=3
Clearly n, 3*n, 5*n  are  three consecutive terms of an arithmetic sequence.

The cubes  of those terms are the  A, B and C - none of which is a perfect cube.
(A, B, C)=(3,81,375)

  Posted by Ady TZIDON on 2013-09-29 10:59:09
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