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Let X be a subset of the integers from 1 to 1997 such that |X|≥34. Show...

Let X be a subset of the integers from 1 to 1997 such that |X|≥34. Show that there exists distinct a,b,c∈X and distinct x,y,z∈X such that a+b+c=x+y+z and {a,b,c}≠{x,y,z}.

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