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IMO 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 ?

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