The new elementary solution of the Waring problem
Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 4, pp. 1239-1252.

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In this paper a new elementary solution of the Waring problem is presented. Waring problem asserts that for any positive integer $k$ there exists a positive integer $n$ such that any positive integer can be presented as the sum of $n$ $k$-th powers of nonnegative integers.
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     author = {A. Bufetov and A. Ya. Kanel'},
     title = {The new elementary solution of the {Waring} problem},
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A. Bufetov; A. Ya. Kanel'. The new elementary solution of the Waring problem. Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 4, pp. 1239-1252. http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a20/