Geodesic
An estimate of the number of terms in Waring's problem for polynomials of general form
Izvestiya. Mathematics , Tome 29 (1987) no. 2, pp. 371-406

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A sharp upper bound is established for the smallest $s$ for which the equation $f(x_1)+\dots+f(x_s)=N$ is solvable in nonnegative integers $x_1,\dots,x_s$ for any fixed integer-valued polynomial $f(x)=a_n\binom xn+\dots+a_1\binom x1$ with $(a_n,\dots,a_1)=1$ and $a_n>0$ for all natural $N\geqslant N_0(f)$. Bibliography: 44 titles. 
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     author = {D. A. Mit'kin},
     title = {An estimate of the number of terms in {Waring's} problem for polynomials of general form},
     journal = {Izvestiya. Mathematics },
     pages = {371--406},
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     volume = {29},
     number = {2},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1987_29_2_a5/}
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D. A. Mit'kin. An estimate of the number of terms in Waring's problem for polynomials of general form. Izvestiya. Mathematics , Tome 29 (1987) no. 2, pp. 371-406. http://geodesic.mathdoc.fr/item/IM2_1987_29_2_a5/