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

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.

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.

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DOI : https://doi.org/10.5802/jtnb.951
Classification : 11P32,  11N36
Mots clés : Waring–Goldbach problem, circle method, sieve method, almost-prime
@article{JTNB_2016__28_2_523_0,
     author = {Xiaodong L\"u and Quanwu Mu},
     title = {On {Waring{\textendash}Goldbach} problem of mixed powers},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {523--538},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {28},
     number = {2},
     year = {2016},
     doi = {10.5802/jtnb.951},
     mrnumber = {3509722},
     zbl = {1415.11129},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.951/}
}
Xiaodong Lü; Quanwu Mu. On Waring–Goldbach problem of mixed powers. Journal de Théorie des Nombres de Bordeaux, Tome 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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