How can I solve this 2014 RMO question with an extremely short method? – math.stackexchange.com

How can I solve this 2014 RMO question with an extremely short method? – math.stackexchange.com

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I was solving a question from the RMO, 2014. Find all positive real numbers $x,y,z$ such that $$2x-2y+\frac1z=\frac1{2014},\quad2y-2z+\frac1x=\frac1{2014},\quad2z-2x+\frac1y=\frac1{2014}$$ Here's ...

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