Geodesic
On One Property of the Weighed Sums of Equal Powers as Matrix Products
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 313-317.

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Finite sum of weighted sum of equal powers is represented in matrix form. This is expressed by the presence of two matrix components, the first of which does not contain, and the second contains the specified weights. It is significant that if the maximum power grounds in the amounts of this type has a value of no less important exponent related to its term, the first matrix component is the same for all amounts that meet the specified condition. Revealed common property of the matrix representation used to obtain the modified final sum from the increased number of weights.
Keywords: finite sum of the weighed equal powers, weight factors, matrix component, modified finite sum. 
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A. I. Nikonov. On One Property of the Weighed Sums of Equal Powers as Matrix Products. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 313-317. http://geodesic.mathdoc.fr/item/VSGTU_2010_5_a39/

[1] Nikonov A. I., “Preobrazovanie summy vzveshennykh stepenei naturalnykh chisel s odinakovymi pokazatelyami”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2010, no. 1(20), 258–262 | DOI

[2] Streng G., Lineinaya algebra i ee primeneniya, Mir, M., 1980, 456 pp. | MR