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2009 a cube? Baseless! (Posted on 2009-03-09) Difficulty: 2 of 5
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.

See The Solution Submitted by K Sengupta    
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re(2): analytic solution - doubt | Comment 4 of 5 |
(In reply to re: analytic solution - doubt by pcbouhid)

The base in Daniel's analysis was m, which varied in Daniel's analysis, to show that 2009, which in base m means 2*m^3+9, cannot be a perfect cube. Mod 9 shows this for all m.
  Posted by Charlie on 2009-03-10 11:21:35

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