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Two results on unlike powers of primes and powers of 2 in the Waring–Goldbach problem

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Abstract

In this paper, we obtain when \(k=26\), every sufficiently large even integer can be represented as a sum of two prime squares, four prime cubes and k powers of 2. What is more, when \(k=58\), every sufficiently large odd integer can be represented as a sum of one prime, four prime cubes and k powers of 2. These improve previous results.

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Acknowledgements

The authors would like to express their thanks to the referee for many useful suggestions and comments on the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330031, Jiangxi, People’s Republic of China

    Liqun Hu

  2. Institute of Mathematics and Interdisciplinary Sciences, Nanchang University, Nanchang, 330031, Jiangxi, People’s Republic of China

    Liqun Hu

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  1. Liqun Hu
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Correspondence to Liqun Hu.

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This work is supported by Natural Science Foundation of Jiangxi Province for Distinguished Young Scholars (Grant Nos. 20212ACB211007), Natural Science Foundation of China (Grant Nos. 11761048) and Natural Science Foundation of Tianjin City (Grant Nos. 19JCQNJC14200).

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Hu, L. Two results on unlike powers of primes and powers of 2 in the Waring–Goldbach problem. Ramanujan J 60, 1081–1094 (2023). https://doi.org/10.1007/s11139-022-00631-y

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  • DOI: https://doi.org/10.1007/s11139-022-00631-y

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