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On the Waring–Goldbach Problem: Exceptional Sets for Sums of Cubes and Higher Powers

open access: yesCanadian Journal of Mathematics - Journal Canadien de Mathematiques, 2005
A. Kumchev
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Exceptional sets in Waring-Goldbach problem for fifth powers [PDF]

open access: yesDoklady Mathematics, 2021
The author considers the following problem: given a natural number \(n\geq 2\), find \(V(n)\) such that, for all sufficiently large integers \(N\), the following representation holds: \[ N=p_{1}^{n}+p_{2}^{n}+\ldots+p_{k}^{n}, \quad \text{with} \,k\leq V(n) \] where the variables \(p_j\) are prime numbers.
Zhenzhen Feng, Zhixin Liu
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Waring-Goldbach Problem for Unlike Powers

open access: yesChinese Annals of Mathematics, Series B, 2019
In this paper, the authors investigate exceptional sets in the Waring-Goldbach problem for unlike powers. For example, estimates are obtained for sufficiently large integers below a parameter subject to the necessary local conditions that do not have a ...
Zhenzhen Feng, Jing Ma
semanticscholar   +3 more sources
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The Waring–Goldbach problem for cubes with an almost prime

Proceedings of the London Mathematical Society, 2019
We show that every sufficiently large even integer can be written as the sum of eight cubes, seven of which are cubes of primes, and the remaining one is that of the product of two primes.
K. Kawada, Lilu Zhao
semanticscholar   +3 more sources

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