# 100 Followers problem!

Algebra Level 4

There are 2011 positive numbers with both their sum and the sum of their reciprocals equal to 2012. Let $$x$$ be one of these numbers, if the maximum value of $$x +\dfrac{1}{x}$$ can be expressed as $$\frac ab$$ for coprime positive integers, submit your answer as $$a-b$$.

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