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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 5, Pages 1015–1053 (Mi izv1562)  

This article is cited in 3 scientific papers (total in 3 papers)

An estimate of the number of terms in Waring's problem for polynomials of general form

D. A. Mit'kin


Abstract: A sharp upper bound is established for the smallest $s$ for which the equation $f(x_1)+…+f(x_s)=N$ is solvable in nonnegative integers $x_1,…,x_s$ for any fixed integer-valued polynomial $f(x)=a_n\binom xn+…+a_1\binom x1$ with $(a_n,…,a_1)=1$ and $a_n>0$ for all natural $N\geqslant N_0(f)$.
Bibliography: 44 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:2, 371–406

Bibliographic databases:

UDC: 511
MSC: Primary 11P05, 11D72; Secondary 11P55, 11D79, 11D85, 11L40
Received: 27.09.1984

Citation: D. A. Mit'kin, “An estimate of the number of terms in Waring's problem for polynomials of general form”, Izv. Akad. Nauk SSSR Ser. Mat., 50:5 (1986), 1015–1053; Math. USSR-Izv., 29:2 (1987), 371–406

Citation in format AMSBIB
\Bibitem{Mit86}
\by D.~A.~Mit'kin
\paper An estimate of the number of terms in Waring's problem for polynomials of general form
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 5
\pages 1015--1053
\mathnet{http://mi.mathnet.ru/izv1562}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=873659}
\zmath{https://zbmath.org/?q=an:0634.10019|0616.10014}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 2
\pages 371--406
\crossref{https://doi.org/10.1070/IM1987v029n02ABEH000975}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. P. Alutin, “Representation of natural numbers as the sum of values of polynomials of primes”, Math. Notes, 58:4 (1995), 1117–1121  mathnet  crossref  mathscinet  zmath  isi
    2. B. G. Fedorischev, “K probleme Varinga dlya nechetnykh mnogochlenov”, Chebyshevskii sb., 8:2 (2007), 109–120  mathnet  mathscinet  zmath
    3. B. G. Fedorischev, “Nekotorye svoistva $p^k$-nechetnykh tseloznachnykh mnogochlenov”, Chebyshevskii sb., 8:2 (2007), 121–127  mathnet  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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