IMO Shortlist 2001 problem N2


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2. travnja 2012.
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Consider the system x + y  = z + u, 2xy = zu. Find the greatest value of the real constant m such that m \leq x/y for any positive integer solution (x,y,z,u) of the system, with x \geq y.
Izvor: Međunarodna matematička olimpijada, shortlist 2001