Brüdern, Jörg A problem in additive number theory. (English) Zbl 0655.10041 Math. Proc. Camb. Philos. Soc. 103, No. 1, 27-33 (1988). The author shows that all sufficiently large natural numbers n can be expressed as the sum \(n=x^ 2_ 1+...+x^{18}_{17}\) of successive powers of natural numbers. This improves an earlier result of the author [J. Lond. Math. Soc., II. Ser. 35, 244-250 (1987; Zbl 0589.10049)]. Reviewer: M.Dodson Cited in 3 ReviewsCited in 33 Documents MSC: 11P05 Waring’s problem and variants 11P55 Applications of the Hardy-Littlewood method 11D85 Representation problems Keywords:representation of integers; large integers; mixed powers; Weyl’s inequality for quadratic exponential sum; cubic sum; mean-value estimate; Hua’s lemma; major arcs; Hardy-Littlewood method Citations:Zbl 0589.10049 PDFBibTeX XMLCite \textit{J. Brüdern}, Math. Proc. Camb. Philos. Soc. 103, No. 1, 27--33 (1988; Zbl 0655.10041) Full Text: DOI References: [1] DOI: 10.1112/plms/s3-52.3.445 · Zbl 0601.10035 · doi:10.1112/plms/s3-52.3.445 [2] Vaughan, Topics in Classical Number Theory pp 1585– (1984) [3] Vaughan, The Hardy?Littlewood Method (1981) · Zbl 0455.10034 [4] DOI: 10.1112/jlms/s2-35.2.233 · Zbl 0589.10048 · doi:10.1112/jlms/s2-35.2.233 [5] Hardy, An Introduction to the Theory of Numbers (1979) · Zbl 0423.10001 [6] DOI: 10.1112/jlms/s2-35.2.244 · Zbl 0589.10049 · doi:10.1112/jlms/s2-35.2.244 [7] Thanigasalam, Acta Arith. 36 pp 125– (1980) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.