# 6000th Brilliant Problem Solved - Problem

Geometry Level 5

Find the largest constant $$m$$ and the smallest constant $$M$$, such that given any 13 distinct real numbers, there always exists 2 numbers $$x$$ and $$y$$, with $$x > y$$, such that

$m < \dfrac {x-y}{1+xy} < M.$

If the value of $$m+M$$ can be written as $$a+b\sqrt{c}$$, where $$a$$, $$b$$ and $$c$$ are integers, and $$c$$ is square-free, find $$a+b+c$$.

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