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Math Help - Help with proof?

  1. #1
    Newbie
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    Mar 2011
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    Help with proof?

    Let x1, x2, . . . , xk be real numbers such that the set A = {cos(nπx1)+cos(nπx2)+
    ˇ ˇ ˇ+cos(nπxk) | n ≥ 1} is finite. Prove that all the xi are rational numbers.

    Apparently, it requires use of the pigeonhole principle, but I can't seem to figure out where or how to apply it
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  2. #2
    Newbie kira's Avatar
    Joined
    Nov 2010
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    apparently , its a question fromt he book 'putnam ad beyond' by titu anreescuu

    http://aam.org.in/st_material/1.pdf

    the solution is in page number 340
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