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2009 a cube? Baseless! (Posted on 20090309) 

Can the base M number 2009 be a perfect cube, where M is a positive integer ≥ 2?
If the answer is yes, give an example. Otherwise prove that the base M number 2009 can never be a perfect cube.

Submitted by K Sengupta

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Solution:

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There was a typing error in the problem text, and the said text should read as:
"Can the base M number 2009 be a perfect cube, where M is a positive integer ≥ 10?" instead of "........M is a positive integer ≥ 2?"
The answer to the problem is that the base M number 2009 can never be a perfect cube.
This has been proved by Daniel in this location.

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