perplexus.info :: Just Math : Imperfectly Cubed

Imperfectly Cubed (Posted on 2013-09-29)

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-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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