Write on the board the equation

$$
(x-1)(x-2) \cdots(x-2016)=(x-1)(x-2) \cdots(x-2016)
$$

where each side has 2016 linear factors. What is the smallest positive value of $k$ for which it is true that we can omit exactly $k$ of the 4032 linear factors so that at least one linear factor remains on each side, and the resulting equation has no real roots?