On the Waring-Goldbach Problem for One Square and Five Cubes

2017/07/25 by Li, Jinjiang, Zhang, Min
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1707.07808

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=x²+p₁³+p₂³+p₃³+p₄³+p₅³ is solvable with x being an almost-prime P₆ and the other variables primes. This result constitutes an improvement upon that of Cai, who obtained the same conclusion, but with P₃₆ in place of P₆.

Related

• Waring-Goldbach Problem: One Square, Four Cubes and Higher Powers
• On Waring-Goldbach Problem for Squares, Cubes and Higher Powers
• Cubic Waring-Goldbach problem with Piatetski-Shapiro primes
• Problems related to Waring-Goldbach problem involving cubes of primes
• On Waring-Goldbach problem for one square and seventeen fifth powers of primes