On Waring–Goldbach problem of mixed powers
Journal de Théorie des Nombres de Bordeaux, Volume 28 (2016) no. 2, pp. 523-538.

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 odd integer N, the equation

N=x2+p13+p23+p33+p43+p56+p67

is solvable with x being an almost-prime P 42 and the other terms powers of primes.

Un nombre presque premier est un P r s’il a au plus r facteurs premiers, comptés avec multiplicité. Dans cet article nous montrons que pour tout entier impair N suffisamment grand, l’équation

N=x2+p13+p23+p33+p43+p56+p67

admet une solution avec x un nombre presque premier P 42 et les autres termes étant des puissances de nombres premiers.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.951
Classification: 11P32,  11N36
Keywords: Waring–Goldbach problem, circle method, sieve method, almost-prime
Xiaodong Lü 1; Quanwu Mu 2

1 Department of Mathematics Tongji University Shanghai, 200092, P. R. China
2 School of Science Xi’an Polytechnic University Xi’an, Shaanxi Province, 710048, P. R. China
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Xiaodong Lü; Quanwu Mu. On Waring–Goldbach problem of mixed powers. Journal de Théorie des Nombres de Bordeaux, Volume 28 (2016) no. 2, pp. 523-538. doi : 10.5802/jtnb.951. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.951/

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