标题：An improvement on Waring-Goldbach problem for unlike powers
作者机构：School of Mathematics, Shandong University, Ji\'nan 250100, China
来源：Acta mathematica Hungarica
关键词：circle method;exceptional set;Waring-Goldbach problem
摘要：Let pi be prime numbers. In this paper, it is proved that for any integer k≧5, with at most O, exceptions, all positive even integers up to N can be expressed in the form p22+p33+p55+pkk. This improves the result O, for some c>0 due to Lu and Shan , and it is a generalization for a series of results of Ren and Tsang ,  and Bauer [1-4] for the problem in the form p22+p33+p44+p55. This method can also be used for some other similar forms.