IMO 2016 Problem 5

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IMO 2016 Problem 5

Post Number:#1  Unread postby Phlembac Adib Hasan » Sun Aug 07, 2016 1:05 pm

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?
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Phlembac Adib Hasan
 
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