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Research Article | Open Access

Exceptional set in Waring–Goldbach problem for sums of one square and five cubes

Jinjiang Li1, Yiyang Pan1, Ran Song1, Min Zhang2( )
Department of Mathematics, China University of Mining and Technology, Beijing 100083, China
School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
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Abstract

Let N be a sufficiently large integer. In this paper, it is proved that, with at most O ( N 4 / 9 + ε ) exceptions, all even positive integers up to N can be represented in the form p 1 2 + p 2 3 + p 3 3 + p 4 3 + p 5 3 + p 6 3 , where p 1 , p 2 , p 3 , p 4 , p 5 , p 6 are prime numbers.

Keywords

Waring–Goldbach problemcircle methodexceptional set
CLC number: 11P05, 11P32, 11P55

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 2940-2955
DOI: 10.3934/math.2022162

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Cite this article:
Li J, Pan Y, Song R, et al. Exceptional set in Waring–Goldbach problem for sums of one square and five cubes. AIMS Mathematics, 2022, 7(2): 2940-2955. https://doi.org/10.3934/math.2022162

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Received: 31 July 2021
Accepted: 15 November 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)