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The method of the unilateral weighed smoothing of time numbers on the basis of use of the polygonal numbers, showing utility of appendices of methods of the additive theory of numbers and calculations of final differences is developed. This method of calculation of weight factors for sliding averaging is based on generalization of the decision of one A.A. Markov's problem. Proposed are the formulas of natural mathematical substantiation in the form of establishing the strictly limiting parities. The comparative an...