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## International Mathematical Olympiad 2016 Problem 5

The equation

$(x-1)(x-2)(x-3)...(x-2016) = (x-1)(x-2)(x-3)...(x-2016)$

is written on a board, with 2016 linear factors on each side. What is the least possible value of $k$ for which it is possible to erase exactly $k$ of these 4032 factors so that at least one factor remains on each side and the resulting equation has no real solutions ?