An elementary estimate of G(n) in Waring's problem

Bredikhin, B. M.; Гришина, Т. И.

doi:10.1007/bf01812976

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Proof Of Theorem1

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1986

2023

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Cited by 3 publications

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“…V. Linnik and B. M. Bredikhin [2] the authors suggested for the first time that one can apply Linnik's dispersion method to solve Waring's problem by elementary means. This idea was realized in 1978 in [1], where an elementary solution of Waring's problem was given, with the estimate…”

Section: Proof Of Theoremmentioning

confidence: 99%

See 1 more Smart Citation

On Waring’s problem (elementary methods)

Nesterenko

2006

J Math Sci

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The paper deals with two elementary methods for solving Waring's problem on the representation of numbers as a sum of equal exponents in powers of natural numbers. The first method is an elementary version of the original Hilbert's proof, and the second one simplifies and makes more precise the elementary Linnik's proof based on the estimate of the number of solutions of a certain system of Diophantine equations. Bibliography: 21 titles.

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Section: Proof Of Theoremmentioning

confidence: 99%

“…25] by efforts of many mathematicians. The proofs were based on more and more complicated identities similar to identity (1). In 1909, in [13] D. Hilbert has proved the following theorem.…”

Section: Introductionmentioning

confidence: 99%