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DK-GEORGMOHR 2019 Problem 2

    Two distinct numbers a and b satisfy that the two equations x2019+ax+2b=0x^{2019} + ax + 2b = 0 and x2019+bx+2a=0x^{2019}+ bx + 2a = 0 have a common solution. Determine all possible values of a+ba + b .

    Dataset text AI-MO AoPS. Quoted with source.

    Official text: Georg Mohr Contest 2019 official paper, page 1.

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