Bài toán Waring (Vietnamese Wikipedia)

Analysis of information sources in references of the Wikipedia article "Bài toán Waring" in Vietnamese language version.

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10doi.org

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8ams.org

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2uni-goettingen.de

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2archive.org

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2harvard.edu

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1zbmath.org

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ams.org

Hilbert, David (1909). “Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem)”. Mathematische Annalen (bằng tiếng Đức). 67 (3): 281–300. doi:10.1007/bf01450405. MR 1511530.
Balasubramanian, Ramachandran; Deshouillers, Jean-Marc; Dress, François (1986). “Problème de Waring pour les bicarrés. I. Schéma de la solution” [Waring's problem for biquadrates. I. Sketch of the solution]. Comptes Rendus de l'Académie des Sciences, Série I (bằng tiếng Pháp). 303 (4): 85–88. MR 0853592.
Balasubramanian, Ramachandran; Deshouillers, Jean-Marc; Dress, François (1986). “Problème de Waring pour les bicarrés. II. Résultats auxiliaires pour le théorème asymptotique” [Waring's problem for biquadrates. II. Auxiliary results for the asymptotic theorem]. Comptes Rendus de l'Académie des Sciences, Série I (bằng tiếng Pháp). 303 (5): 161–163. MR 0854724.
Pillai, S. S. (1940). “On Waring's problem g(6) = 73”. Proc. Indian Acad. Sci. 12: 30–40. doi:10.1007/BF03170721. MR 0002993.
Niven, Ivan M. (1944). “An unsolved case of the Waring problem”. American Journal of Mathematics. The Johns Hopkins University Press. 66 (1): 137–143. doi:10.2307/2371901. JSTOR 2371901. MR 0009386.
Mahler, Kurt (1957). “On the fractional parts of the powers of a rational number II”. Mathematika. 4 (2): 122–124. doi:10.1112/s0025579300001170. MR 0093509.
Kubina, Jeffrey M.; Wunderlich, Marvin C. (1990). “Extending Waring's conjecture to 471,600,000”. Math. Comp. 55 (192): 815–820. Bibcode:1990MaCom..55..815K. doi:10.2307/2008448. JSTOR 2008448. MR 1035936.
Vaughan, R. C.; Wooley, Trevor (2002). “Waring's Problem: A Survey”. Trong Bennet, Michael A.; Berndt, Bruce C.; Boston, Nigel; Diamond, Harold G.; Hildebrand, Adolf J.; Philipp, Walter (biên tập). Number Theory for the Millennium. III. Natick, MA: A. K. Peters. tr. 301–340. ISBN 978-1-56881-152-9. MR 1956283.

archive.org

L. Euler, "Opera posthuma" (1), 203–204 (1862).
Niven, Ivan M. (1944). “An unsolved case of the Waring problem”. American Journal of Mathematics. The Johns Hopkins University Press. 66 (1): 137–143. doi:10.2307/2371901. JSTOR 2371901. MR 0009386.

doi.org

Hilbert, David (1909). “Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem)”. Mathematische Annalen (bằng tiếng Đức). 67 (3): 281–300. doi:10.1007/bf01450405. MR 1511530.
Wieferich, Arthur (1909). “Beweis des Satzes, daß sich eine jede ganze Zahl als Summe von höchstens neun positiven Kuben darstellen läßt”. Mathematische Annalen (bằng tiếng Đức). 66 (1): 95–101. doi:10.1007/BF01450913.
Kempner, Aubrey (1912). “Bemerkungen zum Waringschen Problem”. Mathematische Annalen (bằng tiếng Đức). 72 (3): 387–399. doi:10.1007/BF01456723.^{[liên kết hỏng]}
Pillai, S. S. (1940). “On Waring's problem g(6) = 73”. Proc. Indian Acad. Sci. 12: 30–40. doi:10.1007/BF03170721. MR 0002993.
Niven, Ivan M. (1944). “An unsolved case of the Waring problem”. American Journal of Mathematics. The Johns Hopkins University Press. 66 (1): 137–143. doi:10.2307/2371901. JSTOR 2371901. MR 0009386.
Mahler, Kurt (1957). “On the fractional parts of the powers of a rational number II”. Mathematika. 4 (2): 122–124. doi:10.1112/s0025579300001170. MR 0093509.
Kubina, Jeffrey M.; Wunderlich, Marvin C. (1990). “Extending Waring's conjecture to 471,600,000”. Math. Comp. 55 (192): 815–820. Bibcode:1990MaCom..55..815K. doi:10.2307/2008448. JSTOR 2008448. MR 1035936.
Deshouillers, Jean-Marc; Hennecart, François; Landreau, Bernard; I. Gusti Putu Purnaba, Appendix by (2000). “7373170279850”. Mathematics of Computation. 69 (229): 421–439. doi:10.1090/S0025-5718-99-01116-3.
Deshouillers, Jean-Marc; Hennecart, François; Landreau, Bernard (2000). “Waring's Problem for sixteen biquadrates – numerical results”. Journal de théorie des nombres de Bordeaux. 12 (2): 411–422. doi:10.5802/jtnb.287.
Karatsuba, A. A. (1985). “On the function G(n) in Waring's problem”. Izv. Akad. Nauk SSSR, Ser. Math. 27 (49:5): 935–947. Bibcode:1986IzMat..27..239K. doi:10.1070/IM1986v027n02ABEH001176.

ethz.ch

math.ethz.ch

Deshouillers, Jean-Marc; Hennecart, François; Landreau, Bernard (2000). “Waring's Problem for sixteen biquadrates – numerical results”. Journal de théorie des nombres de Bordeaux. 12 (2): 411–422. doi:10.5802/jtnb.287.

harvard.edu

ui.adsabs.harvard.edu

Kubina, Jeffrey M.; Wunderlich, Marvin C. (1990). “Extending Waring's conjecture to 471,600,000”. Math. Comp. 55 (192): 815–820. Bibcode:1990MaCom..55..815K. doi:10.2307/2008448. JSTOR 2008448. MR 1035936.
Karatsuba, A. A. (1985). “On the function G(n) in Waring's problem”. Izv. Akad. Nauk SSSR, Ser. Math. 27 (49:5): 935–947. Bibcode:1986IzMat..27..239K. doi:10.1070/IM1986v027n02ABEH001176.

jstor.org

Niven, Ivan M. (1944). “An unsolved case of the Waring problem”. American Journal of Mathematics. The Johns Hopkins University Press. 66 (1): 137–143. doi:10.2307/2371901. JSTOR 2371901. MR 0009386.
Kubina, Jeffrey M.; Wunderlich, Marvin C. (1990). “Extending Waring's conjecture to 471,600,000”. Math. Comp. 55 (192): 815–820. Bibcode:1990MaCom..55..815K. doi:10.2307/2008448. JSTOR 2008448. MR 1035936.

uni-goettingen.de

dz-srv1.sub.uni-goettingen.de

Wieferich, Arthur (1909). “Beweis des Satzes, daß sich eine jede ganze Zahl als Summe von höchstens neun positiven Kuben darstellen läßt”. Mathematische Annalen (bằng tiếng Đức). 66 (1): 95–101. doi:10.1007/BF01450913.
Kempner, Aubrey (1912). “Bemerkungen zum Waringschen Problem”. Mathematische Annalen (bằng tiếng Đức). 72 (3): 387–399. doi:10.1007/BF01456723.^{[liên kết hỏng]}

zbmath.org

Vaughan, R. C. (1997). The Hardy–Littlewood method. Cambridge Tracts in Mathematics. 125 (ấn bản thứ 2). Cambridge: Cambridge University Press. ISBN 0-521-57347-5. Zbl 0868.11046.

zenodo.org

Hilbert, David (1909). “Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem)”. Mathematische Annalen (bằng tiếng Đức). 67 (3): 281–300. doi:10.1007/bf01450405. MR 1511530.