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Research Article | Open Access

On the Waring–Goldbach problem for two squares and four cubes

School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
Department of Mathematics, China University of Mining and Technology, Beijing 100083, China
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Abstract

Let P r denote an almost–prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even integer N, the following equation

N = p 1 2 + p 2 2 + x 3 + p 3 3 + p 4 3 + p 5 3

is solvable with x being an almost–prime P 7 and the other variables primes. This result constitutes a deepening upon that of previous results.

Keywords

Waring–Goldbach problemHardy–Littlewood methodsieve methodalmost–prime
CLC number: 11N36, 11P05, 11P32, 11P55

References

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AIMS Mathematics
Volume 7 Issue 7,
July 2022
Pages 12415-12436
DOI: 10.3934/math.2022689

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Cite this article:
Zhang M, Xue F, Li J. On the Waring–Goldbach problem for two squares and four cubes. AIMS Mathematics, 2022, 7(7): 12415-12436. https://doi.org/10.3934/math.2022689

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Received: 04 December 2021
Revised: 18 April 2022
Accepted: 18 April 2022
Published: 15 July 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)