IMO Shortlist 2012 problem N4


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3. studenoga 2013.
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An integer a is called friendly if the equation (m^2+n)(n^2+m)=a(m-n)^3 has a solution over the positive integers.
a) Prove that there are at least 500 friendly integers in the set \{ 1,2,\ldots ,2012\}.
b) Decide whether a=2 is friendly.
Izvor: Međunarodna matematička olimpijada, shortlist 2012