Puzzle
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Ponder This Challenge - August 2005 - first N digits of M is divisible by N

Ponder This Challenge:

Puzzle for August 2005.

This month's puzzle was sent in by Rajesh.
It has appeared elsewhere; attributions will be given with the solution.
We are not asking for solutions this month.

For K as large as possible, produce a K-digit integer M such that for each N=1,2,...,K, the integer given by the first N digits of M is divisible by N.

An example is K=4, M=7084, because 7 is divisible by 1; 70 is divisible by 2; 708 is divisible by 3; and 7084 is divisible by 4.

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