素变量具有特殊形式的哥德巴赫问题  

The Goldbach Problems with Prime Numbers of Special Type

作　　者：孟宪萌[1] 

机构地区：[1]山东财政学院统计与数理学院,济南250014

出　　处：《数学学报（中文版）》2007年第2期255-260,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家科技部973项目(2007CB807903)

摘　　要：设P_k表示素因子个数不超过k的殆素数．本文证明了对几乎所有充分大的偶数n≠2(mod6),方程n=p_1+p_2有素数解p_1,p_2,且p_1+2=P_3;对任何充分大的奇数N≠1(mod6),方程N=p_1+p_2+p_3有素数解p_1,p_2,p_3,且p_2+2=P_3, p_3+2=P_2．Let Pk denote any integer with no more than k prime factors, counted according to multiplicity. It is proved that for almost all sufficiently large even integers n≠ 2 （mod6）, the equation n = P1＋P2 has a solution in prime variables p1,p2 such that P2 ＋ 2 = P3. For every sufficiently large odd integer N≠1 （mod6）, the equation N=p1 ＋P2 ＋P3 has a solution in prime variables P1, P2, P3 such that P2 ＋2=P3, P3＋2=P2.

关 键 词：圆法 筛法 哥德巴赫问题 

分 类 号：O156.4[理学—数学]