The Ramanujan Journal

, Volume 34, Issue 1, pp 57–72 | Cite as

The Waring–Goldbach problem: one square and five cubes

Article
First Online:
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Accepted:

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.

Keywords

Waring–Goldbach problem Hardy–Littlewood method Almost-prime Sieve theory 

Mathematics Subject Classification

11P32 11N36 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsTongji UniversityShanghaiP.R. China

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