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On Hilbert’s solution of Waring’s problem. (English) Zbl 1276.11161

By elementary (no “circle” method allowed), albeit clever, methods the author gives an upper bound \(B(k)\) for the minimal number \(g(k)\) of \(k\)-th powers necessary to write any positive integer as as sum of \(g(k)\) \(k\)-th powers of positive integers. Indeed \[ B(k) := k^{(15+o(1))(2k)^{5}}, \] improving on previous results of this kind. Some historical background on the problem is recalled.

MSC:

11P05 Waring’s problem and variants
11C08 Polynomials in number theory
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References:

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