Y by Adventure10, Mango247
Let
be an continuous function defined in ![$\text{[0,2015]},f(0)=f(2015)$](//latex.artofproblemsolving.com/c/9/9/c99f63e726b504aea8c1a65ba2926155a873effa.png)
Prove that there exists at least
pairs of
such that 

![$\text{[0,2015]},f(0)=f(2015)$](http://latex.artofproblemsolving.com/c/9/9/c99f63e726b504aea8c1a65ba2926155a873effa.png)
Prove that there exists at least



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