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Abstract: Let be the kth moment of the number of integers coprime to q in an interval of length h centered on its mean . By comparison with the kth centered moment of the binomial distribution with parameters h and P, for which we show uniformly in k, h and P and where is an absolute constant, we prove the following upper bound where is an absolute constant, uniformly in k, h and q provided that every prime factor of q is greater than or equal to h. [Copyright &y& Elsevier]