Question 5
The equation $$
(x-1)(x-2)\dots(x-2016)=(x-1)(x-2)\dots (x-2016)
$$ 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?
(x-1)(x-2)\dots(x-2016)=(x-1)(x-2)\dots (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?