Rocky Mountain Journal of Mathematics

On a Waring-Goldbach problem for mixed powers

Yingjie Li and Yingchun Cai

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Let $P_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved, among other results, that, for every sufficiently large, even integer $N$ satisfying the congruence condition $N \not \equiv 2\pmod 3$, the equation \[ N=x^2+p^2+p_1^3+p_2^4+p_3^4+p_4^4 \] is solvable with $x$ being a $P_{5}$ and the other variable primes. This result constitutes an enhancement upon that of Vaughan \cite {s12} and Mu \cite {s9}.

Article information

Rocky Mountain J. Math., Volume 47, Number 6 (2017), 1947-1961.

First available in Project Euclid: 21 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11N36: Applications of sieve methods 11P32: Goldbach-type theorems; other additive questions involving primes

Waring-Goldbach problem Hardy-Littlewood method almost-prime sieve theory


Li, Yingjie; Cai, Yingchun. On a Waring-Goldbach problem for mixed powers. Rocky Mountain J. Math. 47 (2017), no. 6, 1947--1961. doi:10.1216/RMJ-2017-47-6-1947.

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