Das, Pranabesh; Dey, Pallab Kanti; Koutsianas, Angelos; Tzanakis, Nikos Perfect powers in sum of three fifth powers. (English) Zbl 1493.11073 J. Number Theory 236, 443-462 (2022). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11D61 11D41 11F11 11F80 PDFBibTeX XMLCite \textit{P. Das} et al., J. Number Theory 236, 443--462 (2022; Zbl 1493.11073) Full Text: DOI arXiv
Cai, Tianxin; Zhang, Yong A variety of Euler’s sum of powers conjecture. (English) Zbl 07442476 Czech. Math. J. 71, No. 4, 1099-1113 (2021). MSC: 11D72 11D41 11G05 PDFBibTeX XMLCite \textit{T. Cai} and \textit{Y. Zhang}, Czech. Math. J. 71, No. 4, 1099--1113 (2021; Zbl 07442476) Full Text: DOI
Choudhry, Ajai New solutions of the Tarry-Escott problem of degrees 2, 3 and 5. (English) Zbl 1479.11057 J. Integer Seq. 24, No. 8, Article 21.8.1, 9 p. (2021). MSC: 11D72 11D25 11D41 PDFBibTeX XMLCite \textit{A. Choudhry}, J. Integer Seq. 24, No. 8, Article 21.8.1, 9 p. (2021; Zbl 1479.11057) Full Text: arXiv Link
Sahukar, Manasi Kumari; Panda, G. K. Arithmetic functions of balancing numbers. (English) Zbl 1448.11009 Fibonacci Q. 56, No. 3, 246-251 (2018). MSC: 11A25 11B39 PDFBibTeX XMLCite \textit{M. K. Sahukar} and \textit{G. K. Panda}, Fibonacci Q. 56, No. 3, 246--251 (2018; Zbl 1448.11009) Full Text: arXiv Link
Reynya, M. A. Representation of a rational number as a sum of ninth or higher odd powers. (English) Zbl 1440.11043 Funct. Approximatio, Comment. Math. 58, No. 1, 79-87 (2018). MSC: 11D72 11P05 PDFBibTeX XMLCite \textit{M. A. Reynya}, Funct. Approximatio, Comment. Math. 58, No. 1, 79--87 (2018; Zbl 1440.11043) Full Text: DOI Euclid
Lu, Da-Qian; Srivastava, H. M. Some series identities involving the generalized Apostol type and related polynomials. (English) Zbl 1236.33020 Comput. Math. Appl. 62, No. 9, 3591-3602 (2011). MSC: 33C45 11B83 PDFBibTeX XMLCite \textit{D.-Q. Lu} and \textit{H. M. Srivastava}, Comput. Math. Appl. 62, No. 9, 3591--3602 (2011; Zbl 1236.33020) Full Text: DOI
Hooley, C. On polynomials that are sums of two perfect \(q\)th powers. (English) Zbl 1220.11046 Acta Arith. 145, No. 1, 1-31 (2010). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D41 11P99 PDFBibTeX XMLCite \textit{C. Hooley}, Acta Arith. 145, No. 1, 1--31 (2010; Zbl 1220.11046) Full Text: DOI
Białynicki-Birula, Andrzej; Schinzel, Andrzej Extreme binary forms. (English) Zbl 1197.11046 Acta Arith. 142, No. 3, 219-249 (2010). Reviewer: Denis Ibadula (Constanta) MSC: 11E76 12E05 11D85 PDFBibTeX XMLCite \textit{A. Białynicki-Birula} and \textit{A. Schinzel}, Acta Arith. 142, No. 3, 219--249 (2010; Zbl 1197.11046) Full Text: DOI
Chlebowicz, Agnieszka; Wołowiec-Musial, Małgorzata Forms with a unique representation as a sum of powers of linear forms. (English) Zbl 1150.11417 Tatra Mt. Math. Publ. 32, 33-39 (2005). Reviewer: Radan Kučera (Brno) MSC: 11E76 PDFBibTeX XMLCite \textit{A. Chlebowicz} and \textit{M. Wołowiec-Musial}, Tatra Mt. Math. Publ. 32, 33--39 (2005; Zbl 1150.11417)
Chipalkatti, Jaydeep The Waring loci of ternary quartics. (English) Zbl 1061.14057 Exp. Math. 13, No. 1, 93-101 (2004). MSC: 14N05 14L35 13A50 13F20 11E76 PDFBibTeX XMLCite \textit{J. Chipalkatti}, Exp. Math. 13, No. 1, 93--101 (2004; Zbl 1061.14057) Full Text: DOI arXiv Euclid EuDML
Sándor, József Geometric theorems, Diophantine equations, and arithmetic functions. (English) Zbl 1004.11001 Rehoboth, NM: American Research Press. 298 p. (2002). Reviewer: Štefan Porubský (Praha) MSC: 11-01 11-06 00B60 11A25 11B75 11B83 11D25 11D41 11D61 26D99 51A99 PDFBibTeX XMLCite \textit{J. Sándor}, Geometric theorems, Diophantine equations, and arithmetic functions. Rehoboth, NM: American Research Press (2002; Zbl 1004.11001) Full Text: viXra
Bernstein, Daniel J. Enumerating solutions to \(p(a)+q(b)=r(c)+s(d)\). (English) Zbl 0960.11055 Math. Comput. 70, No. 233, 389-394 (2001). Reviewer: B.Z.Moroz (Bonn) MSC: 11Y50 11D25 11D41 11P05 PDFBibTeX XMLCite \textit{D. J. Bernstein}, Math. Comput. 70, No. 233, 389--394 (2001; Zbl 0960.11055) Full Text: DOI
Brindza, B.; Pintér, Á. On the number of solutions of the equation \(1^k+2^k+\dots+(x-1)^k=y^z\). (English) Zbl 0961.11011 Publ. Math. Debr. 56, No. 3-4, 271-277 (2000). Reviewer: Ferenc Mátyás (Eger) MSC: 11D61 11D41 11B68 PDFBibTeX XMLCite \textit{B. Brindza} and \textit{Á. Pintér}, Publ. Math. Debr. 56, No. 3--4, 271--277 (2000; Zbl 0961.11011)
Reznick, Bruce Some concrete aspects of Hilbert’s 17th problem. (English) Zbl 0972.11021 Delzell, Charles N. (ed.) et al., Real algebraic geometry and ordered structures. AMS special session, Baton Rouge, LA, USA, April 17-21, 1996 and the associated special semester at Louisiana State University and Southern University, Baton Rouge, LA, USA, January-May 1996. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 253, 251-272 (2000). Reviewer: Danielle Gondard (Paris) MSC: 11E10 12D15 11-02 11-03 11E76 01A60 14P99 PDFBibTeX XMLCite \textit{B. Reznick}, Contemp. Math. 253, 251--272 (2000; Zbl 0972.11021)
Zenkin, A. A. The generalized Waring problem: A new property of positive integers. (English. Russian original) Zbl 0860.11059 Math. Notes 58, No. 3, 933-937 (1995); translation from Mat. Zametki 58, No. 3, 372-378 (1995). Reviewer: L.N.Vaserstein and E.R.Wheland (University Park) MSC: 11P05 PDFBibTeX XMLCite \textit{A. A. Zenkin}, Math. Notes 58, No. 3, 933--937 (1995; Zbl 0860.11059); translation from Mat. Zametki 58, No. 3, 372--378 (1995) Full Text: DOI
Wooley, Trevor D. Large improvements in Waring’s problem. (English) Zbl 0754.11026 Ann. Math. (2) 135, No. 1, 131-164 (1992). Reviewer: J.Brüdern (Göttingen) MSC: 11P05 11P55 11L15 PDFBibTeX XMLCite \textit{T. D. Wooley}, Ann. Math. (2) 135, No. 1, 131--164 (1992; Zbl 0754.11026) Full Text: DOI
Wang, Edward T. H.; Shan, Zun An application of number theory to tournaments. (English) Zbl 0738.05042 Graph theory, combinatorics, algorithms, and applications, Proc. 2nd Int. Conf., San Francisco/CA (USA) 1989, 581-587 (1991). Reviewer: Št.Znám (Bratislava) MSC: 05C20 11E76 PDFBibTeX XMLCite \textit{E. T. H. Wang} and \textit{Z. Shan}, in: Existence theorems for nonseparable \(\alpha\)-valuations of snakes. . 581--587 (1991; Zbl 0738.05042)
Habsieger, L. Représentations des groupes et identités polynomiales. (Representations of groups and polynomial identities). (French) Zbl 0758.11042 Sémin. Théor. Nombres Bordx., Sér. II 3, No. 1, 1-11 (1991). Reviewer: L.N.Vaserstein and E.R.Wheland (University Park) MSC: 11P05 PDFBibTeX XMLCite \textit{L. Habsieger}, Sémin. Théor. Nombres Bordx., Sér. II 3, No. 1, 1--11 (1991; Zbl 0758.11042) Full Text: DOI Numdam EuDML
Paul, E. M. A probabilistic approach to additive number theory. (English) Zbl 0749.11044 Algebra and number theory, Proc. Symp., Kochi/India 1990, Publ., Cent. Math. Sci., Trivandrum 20, 3-4 (1990). Reviewer: M.M.Dodson (Heslington) MSC: 11P05 11K99 PDFBibTeX XMLCite \textit{E. M. Paul}, Publ., Cent. Math. Sci., Trivandrum 20, 3--4 (1990; Zbl 0749.11044)
Kanold, Hans-Joachim On a new generalization of a theorem of L. E. Dickson. (Über eine neue Verallgemeinerung eines Satzes von L. E. Dickson.) (German) Zbl 0671.10004 Arch. Math. 54, No. 5, 448-454 (1990). Reviewer: H.-J.Kanold MSC: 11A25 PDFBibTeX XMLCite \textit{H.-J. Kanold}, Arch. Math. 54, No. 5, 448--454 (1990; Zbl 0671.10004) Full Text: DOI
Bradley, Margarita Convex hull of polynomials and sums of 2m-th powers. (Fermeture convexe de polynômes et sommes de puissances 2m-ièmes). (English) Zbl 0697.12019 C. R. Acad. Sci., Paris, Sér. I 309, No. 12, 751-755 (1989). Reviewer: N.Schwartz MSC: 12J15 11E76 PDFBibTeX XMLCite \textit{M. Bradley}, C. R. Acad. Sci., Paris, Sér. I 309, No. 12, 751--755 (1989; Zbl 0697.12019)
Vaughan, R. C. A new iterative method in Waring’s problem. (English) Zbl 0665.10033 Acta Math. 162, No. 1-2, 1-71 (1989). Reviewer: J.Brüdern MSC: 11P05 11P55 11L40 11N35 PDFBibTeX XMLCite \textit{R. C. Vaughan}, Acta Math. 162, No. 1--2, 1--71 (1989; Zbl 0665.10033) Full Text: DOI
Nunemacher, Jeffrey; Young, Robert M. On the sum of consecutive \(k\)th powers. (English) Zbl 0625.10009 Math. Mag. 60, 237-238 (1987). MSC: 11B68 PDFBibTeX XMLCite \textit{J. Nunemacher} and \textit{R. M. Young}, Math. Mag. 60, 237--238 (1987; Zbl 0625.10009) Full Text: DOI
Chen, Jingrun; Li, Jianyu [Rie, Jienyu] Concerning a general property of the sums of powers of integers. (Chinese) Zbl 0625.10008 J. Math. Res. Expo. 6, No. 1, 43-50 (1986). Reviewer: Ke Zhao (Chengdu) MSC: 11B75 05A19 PDFBibTeX XMLCite \textit{J. Chen} and \textit{J. Li}, J. Math. Res. Expo. 6, No. 1, 43--50 (1986; Zbl 0625.10008)
Lim, Jong In Higher level signatures on valuation rings. (English) Zbl 0597.13006 J. Korean Math. Soc. 23, 83-87 (1986). Reviewer: Robert O. Robson (Corvallis) MSC: 12D15 11E81 13A18 13F99 PDFBibTeX XMLCite \textit{J. I. Lim}, J. Korean Math. Soc. 23, 83--87 (1986; Zbl 0597.13006) Full Text: Link
Nathanson, Melvyn B. Waring’s problem for finite intervals. (English) Zbl 0592.10042 Proc. Am. Math. Soc. 96, 15-17 (1986). Reviewer: J.Zöllner MSC: 11P05 11B13 11B05 PDFBibTeX XMLCite \textit{M. B. Nathanson}, Proc. Am. Math. Soc. 96, 15--17 (1986; Zbl 0592.10042) Full Text: DOI
Bressoud, D. M.; Subbarao, M. V. On Uchimura’s connection between partitions and the number of divisors. (English) Zbl 0536.10013 Can. Math. Bull. 27, 143-145 (1984). Reviewer: K.Thanigasalam MSC: 11P81 11A25 05A15 PDFBibTeX XMLCite \textit{D. M. Bressoud} and \textit{M. V. Subbarao}, Can. Math. Bull. 27, 143--145 (1984; Zbl 0536.10013) Full Text: DOI
Becker, Eberhard; Schwartz, Niels Zum Darstellungssatz von Kadison-Dubois. (German) Zbl 0514.12023 Arch. Math. 40, 421-428 (1983). MSC: 12J15 13J25 46A40 12D15 06F25 46A22 46J05 PDFBibTeX XMLCite \textit{E. Becker} and \textit{N. Schwartz}, Arch. Math. 40, 421--428 (1983; Zbl 0514.12023) Full Text: DOI
Grytczuk, Aleksander On a conjecture of Erdoes. (English) Zbl 0511.10034 Discuss. Math. 5, 45-48 (1982). MSC: 11N05 PDFBibTeX XMLCite \textit{A. Grytczuk}, Discuss. Math. 5, 45--48 (1982; Zbl 0511.10034)
Kaja, Janusz A certain generalization of a result of Erdoes and Suranyi. (English) Zbl 0498.10026 Colloq. Math. 47, 149-151 (1982). MSC: 11P05 PDFBibTeX XMLCite \textit{J. Kaja}, Colloq. Math. 47, 149--151 (1982; Zbl 0498.10026) Full Text: DOI
Becker, Eberhard; Harman, Jonathan; Rosenberg, Alex Signatures of fields and extension theory. (English) Zbl 0466.12007 J. Reine Angew. Math. 330, 53-75 (1982). MSC: 11R52 11R21 16H05 11R33 PDFBibTeX XMLCite \textit{E. Becker} et al., J. Reine Angew. Math. 330, 53--75 (1982; Zbl 0466.12007) Full Text: Crelle EuDML
Craven, Thomas C. Orderings of higher level and semilocal rings. (English) Zbl 0438.13022 Math. Z. 176, 577-588 (1981). Reviewer: Thomas C. Craven (Honolulu) MSC: 11E08 11E81 12D15 12J10 PDFBibTeX XMLCite \textit{T. C. Craven}, Math. Z. 176, 577--588 (1981; Zbl 0438.13022) Full Text: DOI EuDML
Iwata, Hiroshi Some properties of Porges’ functions. (English) Zbl 0185.10404 Proc. Japan Acad. 45, 461-465 (1969). Reviewer: Betty Garrison (San Diego) MSC: 11A63 PDFBibTeX XMLCite \textit{H. Iwata}, Proc. Japan Acad. 45, 461--465 (1969; Zbl 0185.10404) Full Text: DOI
Uchiyama, Saburô On the distribution of integers representable as a sum of two \(h\)-th powers. (English) Zbl 0199.08702 J. Fac. Sci., Hokkaido Univ., Ser. I 18, 124-127 (1964). Reviewer: J. H. van Lint (Eindhoven) MSC: 11N60 PDFBibTeX XMLCite \textit{S. Uchiyama}, J. Fac. Sci., Hokkaido Univ., Ser. I 18, 124--127 (1964; Zbl 0199.08702)
Swetharanyam, S. On the function \(\sigma_k (n)\). (English) Zbl 0082.25604 Ann. Pol. Math. 4, 340-343 (1958). Reviewer: Bengt Stolt (Uppsala) MSC: 11A25 PDFBibTeX XMLCite \textit{S. Swetharanyam}, Ann. Pol. Math. 4, 340--343 (1958; Zbl 0082.25604)
Erdös, P. On the representation of an integer as the sum of \(k\) \(k\)-th powers. (English) JFM 62.1139.01 J. Lond. Math. Soc. 11, 133-136 (1936). Reviewer: Weber, W., Prof. (Berlin) MSC: 11P05 PDFBibTeX XMLCite \textit{P. Erdös}, J. Lond. Math. Soc. 11, 133--136 (1936; JFM 62.1139.01) Full Text: DOI
Welmin, W. P. Solution of the Diophantine equation \(u^m + v^n w^k\). (Lösung der unbestimmten Gleichung \(u^m + v^n = w^k\).) (Russian) JFM 35.0217.01 Moskau Math. Samml. (Mat. Sb.) 24, 633-661 (1904). Reviewer: Sintzow, Prof. (Charkow) MSC: 11D41 11C08 11G99 PDFBibTeX XML
Martin, A. About sixth power numbers whose sum is a sixth power. (About sixth power numbers whose sum is a sixth power.) (English) JFM 35.0203.01 Math. Magazine 2, 265-271 (1904). Reviewer: Lampe, Prof. (Berlin) MSC: 11D85 11D41 11E76 11P99 PDFBibTeX XMLCite \textit{A. Martin}, Math. Magazine 2, 265--271 (1904; JFM 35.0203.01)
Dostor, G. A remarkable identity arising from a sum of fourth powers of four numbers. (Identité remarquable fournie par la quatrième puissance d’une somme de quatre nombres.) (French) JFM 09.0123.04 Grunert Arch. LX, 445-446 (1877). Reviewer: Schlegel, Dr. (Waren) MSC: 11A99 11E76 PDFBibTeX XMLCite \textit{G. Dostor}, Grunert Arch. 60, 445--446 (1877; JFM 09.0123.04)