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Let d(n;l,k) denote the number of divisors of the positive integer n which are congruent to I modulo k. The objective of the present paper is to prove that (for some exponent θ<⅓)
holds uniformly in l, k and x satisfying 1≤l≤k≤x. This improves a recent result due to R. A. Smith and M. V. Subbarao [3].
