1969 IMO Problems/Problem 2
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Let 
be real constants, 
a real variable, and ![\[f(x)=\cos(a_1+x)+\frac{1}{2}\cos(a_2+x)+\frac{1}{4}\cos(a_3+x)+\cdots+\frac{1}{2^{n-1}}\cos(a_n+x).\]](http://latex.artofproblemsolving.com/a/b/9/ab9533ac04d0ae6529faefae8b78bcc83390deee.png)
Given that 
prove that 
for some integer 
