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

2017/08/15 by Jinjiang Li, Min Zhang, Li, Jinjiang +1
Mathematics · #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1708.04484

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 12\leqslant b\leqslant 35 and for every sufficiently large odd integer N, the equation N=x²+p₁³+p₂³+p₃³+p₄³+p₅⁴+p₆^b is solvable with x being an almost-prime P_r(b) and the other variables primes, where r(b) is defined in the Theorem. This result constitutes an improvement upon that of Lü and Mu.

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