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Erdős problem 731

Let A(n)A(n) be the least positive integer not dividing (2nn)\binom{2n}{n}. Erdos asked for the behaviour of A(n)A(n) for reasonable nn. Under an explicit dyadic-regularity formalization of reasonable, the distribution is determined on dyadic intervals against the scale FX=2(log2)1/4L1/4exp(log2)LF_X = \sqrt{2}(\log 2)^{1/4} L^{1/4} \exp\sqrt{(\log 2)L} with L=log(2X)L = \log(2X).

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