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Erdős problem 176

Let N(k,)N(k, \ell) be the least NN such that every f:[N]{1,1}f : [N] \to \{-1, 1\} has a kk-term arithmetic progression PP with nPf(n)|\sum_{n \in P} f(n)| \ge \ell. In particular, is N(k,2)CkN(k, 2) \le C^k?

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