# Year Today, Gone Tomorrow?

Consider the set {1,11,111, …, ((10^2007) – 1)/9}.

Prove at least one of these numbers is divisible by 2007.

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

Communicated by Michael Varnava.

July 12, 2010
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Consider the set {1,11,111, …, ((10^2007) – 1)/9}.

Prove at least one of these numbers is divisible by 2007.

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

Communicated by Michael Varnava.

Warning: Solutions May Be Discussed in the Comments

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