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Is it a factor?

Question

Consider the set {1,11,111, …, ((10^2007) – 1)/9}.  At least one of these numbers is divisible by 2007.

Is the same true for 2008 (replacing 10^2007 with 10^2008, of course)?

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I think…

Spoiler

No. 2008 is an even number (it includes a factor of 2), while each of (10n - 1) / 9 is odd by construction (does not include a factor of 2).

 

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