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.

(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