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CZ-SK-MO 1995 Problem 6

    Find all real parameters pp for which the equation x3−2p(p+1)x2+(p4+4p3−1)x−3p3=0x^3 -2p(p+1)x^2+(p^4 +4p^3 -1)x-3p^3 = 0 has three distinct real roots which are sides of a right triangle.

    Dataset text AI-MO AoPS. Quoted with source.

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