Question 36
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?
$$(x - 1)(x - 2)\cdots(x - 2016) = (x - 1)(x - 2)\cdots(x - 2016)$$
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?