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Product Digit Poser (Posted on 2010-06-13) Difficulty: 3 of 5
Determine all possible values of a positive integer N such that the product of the nonzero digits in the base-N representation of 2009 (base ten) is equal to 18 (base ten).

No Solution Yet Submitted by K Sengupta    
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Hints/Tips post-solution hint (no spoiler) | Comment 2 of 5 |
(In reply to computer solution (spoiler) by Charlie)

In retrospect, it looks as if an analytic solution might be based on factoring 2009 in various possible ways and coming up with polynomials that could be solved a base, though this might still lead to a large number of polynomials to solve given that the order is important, and you don't know how many 0's or 1's to include.
  Posted by Charlie on 2010-06-13 14:45:57

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