BMAD Posted March 16, 2018 Report Share Posted March 16, 2018 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)? Quote Link to comment Share on other sites More sharing options...

1 ThunderCloud Posted March 18, 2018 Report Share Posted March 18, 2018 I think… Spoiler No. 2008 is an even number (it includes a factor of 2), while each of (10^{n} - 1) / 9 is odd by construction (does not include a factor of 2). Quote Link to comment Share on other sites More sharing options...

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## BMAD

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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