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A problem in additive number theory. (English) Zbl 0655.10041

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

MSC:

11P05 Waring’s problem and variants
11P55 Applications of the Hardy-Littlewood method
11D85 Representation problems

Citations:

Zbl 0589.10049
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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)
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