一个关于素变量的四元加性方程

A Quaternary Additive Equation Involving Prime Variables

用[x]表示不超过x的最大整数.本文证明了对于充分大的正整数N以及任意的1<c<14/11,关于素变量P_(1),P_(2),P_(3),P_(4)的加性方程[p^(c)_(1)]+[p^(c)_(2)]+[p^(c)_(3)]+[p^(c)_(4)]=N有无穷多组解.

Let[x]denote the largest integer not exceeding x.It is proved that for 1<c<14/11,the additive equation[p^(c)_(1)]+[p^(c)_(2)]+[p^(c)_(3)]+[p^(c)_(4)]=N has infinitely many solutions in prime variables P_(1),P_(2),P_(3),P_(4)for sufficiently large positive integer N.