Let denote an almost-prime with at most prime factors, counted according to multiplicity. In this paper it is proved that for every sufficiently large odd integer , the equation
is solvable with being an almost-prime and the other terms powers of primes.
Un nombre presque premier est un s’il a au plus facteurs premiers, comptés avec multiplicité. Dans cet article nous montrons que pour tout entier impair suffisamment grand, l’équation
admet une solution avec un nombre presque premier et les autres termes étant des puissances de nombres premiers.
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.951
Keywords: Waring–Goldbach problem, circle method, sieve method, almost-prime
Xiaodong Lü 1; Quanwu Mu 2
@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}, zbl = {1415.11129}, mrnumber = {3509722}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.951/} }
TY - JOUR AU - Xiaodong Lü AU - Quanwu Mu TI - On Waring–Goldbach problem of mixed powers JO - Journal de théorie des nombres de Bordeaux PY - 2016 SP - 523 EP - 538 VL - 28 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.951/ DO - 10.5802/jtnb.951 LA - en ID - JTNB_2016__28_2_523_0 ER -
%0 Journal Article %A Xiaodong Lü %A Quanwu Mu %T On Waring–Goldbach problem of mixed powers %J Journal de théorie des nombres de Bordeaux %D 2016 %P 523-538 %V 28 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.951/ %R 10.5802/jtnb.951 %G en %F JTNB_2016__28_2_523_0
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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