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The Waring–Goldbach problem: one square and five cubes

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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 equation

$$N=x^2+p^3_1+p^3_2+p_3^3+p_4^3+p_5^3 $$

is solvable with x being an almost-prime P 36 and the p j ’s primes. This result constitutes a refinement upon that of G.L. Watson.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, 200092, P.R. China

    Yingchun Cai

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  1. Yingchun Cai
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Correspondence to Yingchun Cai.

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Project supported by the National Natural Science Foundation of China (grant no. 11071186).

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Cai, Y. The Waring–Goldbach problem: one square and five cubes. Ramanujan J 34, 57–72 (2014). https://doi.org/10.1007/s11139-013-9486-y

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  • DOI: https://doi.org/10.1007/s11139-013-9486-y

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