IMO Shortlist 1991 problem 21


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2. travnja 2012.
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Real constants a, b, c are such that there is exactly one square all of whose vertices lie on the cubic curve y = x^3 + ax^2 + bx + c. Prove that the square has sides of length \sqrt[4]{72}.
Izvor: Međunarodna matematička olimpijada, shortlist 1991