Waring-Goldbach Problem: One Square, Four Cubes and Higher Powers

Jinjiang Li; Min Zhang

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arXiv · 1708.04484

Waring-Goldbach Problem: One Square, Four Cubes and Higher Powers

Jinjiang Li·Min Zhang

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Abstract

Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that, for $12\leqslant b\leqslant 35$ and for every sufficiently large odd integer $N$, the equation \begin{equation*} N=x^2+p_1^3+p_2^3+p_3^3+p_4^3+p_5^4+p_6^b \end{equation*} is solvable with $x$ being an almost-prime $\mathcal{P}_{r(b)}$ and the other variables primes, where $r(b)$ is defined in the Theorem. This result constitutes an improvement upon that of L\"u and Mu.

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Jinjiang Li, Min Zhang. 2017-08-15. Waring-Goldbach Problem: One Square, Four Cubes and Higher Powers. https://arxiv.org/abs/1708.04484

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