Tournament Integer!

mm is a positive integer such that mm÷m2\overline{mm} \div m^2 is equal to some integer, kk. What is the sum of all possible values of kk?

Details and assumptions:

aa\overline{aa} means the number obtained by writing aa twice. For example if a=103a=103, then aa=103103\overline{aa}=103103.

This problem appeared in the TOT 2004.

This problem is from the set "Olympiads and Contests Around the World -1". You can see the rest of the problems here.


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