2016 IMO Problems/Problem 5

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The equation

(x-1)(x-2)\cdots(x-2016)=(x-1)(x-2)\cdots (x-2016)$ is written on the 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\$ linear factors so that at least one factor remains on each side and the resulting equation has no real solutions?