Waring-Goldbach problem: two squares and higher powers
Yingchun Cai1
1 Department of Mathematics Tongji University Shanghai, 200092, P. R. China
Journal de théorie des nombres de Bordeaux, Volume 28 (2016) no. 3, pp. 791-810.

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+p2+p15+p25+p35+p45+p55+p65

is solvable with x being a P 6 and the other variables primes. This result constitutes an enhancement upon that of C. Hooley.

Soit P r l’ensemble des nombres presque-premiers avec au plus r facteurs premiers comptés avec avec multiplicité. Dans cet article, on motre que pour tout entier pair N suffisamment grand, l’équation

N=x2+p2+p15+p25+p35+p45+p55+p65

a des solutions avec x un P 6 et les autres étant des nombres premiers. Ceci est une amélioration de résultats antérieurs de C. Hooley.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.964
Classification: 11P32, 11N36
Keywords: Waring-Goldbach problem, Hardy-Littlewood method, sieve theory, almost-prime.
Yingchun Cai 1

1 Department of Mathematics Tongji University Shanghai, 200092, P. R. China 
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Yingchun Cai. Waring-Goldbach problem: two squares and higher powers. Journal de théorie des nombres de Bordeaux, Volume 28 (2016) no. 3, pp. 791-810. doi : 10.5802/jtnb.964. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.964/

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