# Tournament Integer!

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

Details and assumptions:

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

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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