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> Let $A=\{x\_1,x\_2,\cdots,x\_n\}$ be a set of $n$ distinct real numbers. Show that there exists a set $B\subset A$ such that $$|B|\geq\lfloor\sqrt{2n}+\frac12\rfloor$$ and no $3$ distinct elements of $B$ constitute an arithmetic progression.
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I have no idea how to approach this problem, with its strange-looking formula. I've already posted it on AoPS but no reply.