IMO Shortlist 2001 problem N2


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Dodao/la: arhiva
April 2, 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.
Source: Međunarodna matematička olimpijada, shortlist 2001