Difference between revisions of "2016 IMO Problems/Problem 5"

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The equation
 
The equation
<center>(x-1)(x-2)\cdots(x-2016)=(x-1)(x-2)\cdots (x-2016)<math></center>
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<center><math>(x-1)(x-2)\cdots(x-2016)=(x-1)(x-2)\cdots (x-2016)</math></center>
is written on the board, with </math>2016<math> linear factors on each side. What is the least possible value of </math>k<math> for which it is possible to erase exactly </math>k<math> of these </math>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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is written on the board, with <math>2016</math> linear factors on each side. What is the least possible value of <math>k</math> for which it is possible to erase exactly <math>k</math> of these <math>4032</math> linear factors so that at least one factor remains on each side and the resulting equation has no real solutions?

Latest revision as of 20:16, 26 December 2019

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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