The equation
$$
(x-1)(x-2)(x-3)\dots(x-2016)=(x-1)(x-2)(x-3)\dots(x-2016)
$$
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?
[Math] IMO 2016 Problem 5
combinatoricscontest-mathpolynomialsrecreational-mathematicsroots
Best Answer
An interpretation of the solution from here. Sorry my Chinese.