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Prove that there is a positive constant c so that every set A of n nonzero reals contains a subset B C Aofsize|B| > cn so that there are no

Prove that there is a positive constant c so that every set A of n nonzero reals
contains a subset B C Aofsize|B| > cn so that there are no b_1,b_2,b_3, b_4 belong to B
satisfying
b_1 + 2b_2 = 2b_3 + 2b_4 .

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