| 素变量具有特殊形式的哥德巴赫问题 |
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| 引用本文： | 孟宪萌.素变量具有特殊形式的哥德巴赫问题[J].数学学报,2007,50(2):255-260. |
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| 作者姓名： | 孟宪萌 |
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| 作者单位： | 山东财政学院统计与数理学院 济南 |
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| 基金项目： | 国家科技部973项目(2007CB807903) |
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| 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．
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| 关 键 词： | 圆法 筛法 哥德巴赫问题 |
| 文章编号： | 0583-1431（2007）02-0255-06 |
| 收稿时间： | 2005-4-27 |
| 修稿时间： | 2005-04-27 |
The Goldbach Problems with Prime Numbers of Special Type |
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| Xian Meng MENG.The Goldbach Problems with Prime Numbers of Special Type[J].Acta Mathematica Sinica,2007,50(2):255-260. |
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| Authors: | Xian Meng MENG |
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| Institution: | Xian Meng MENG Department of Statistics and Mathematics,Shandong Finance Institute,Ji'nan 250014,P.R.China |
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| Abstract: | Let P_k 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 (mod 6),the equation n=P_1+P_2 has a solution in prime variables P_1,P_2 such that P_2+2=P_3.For every sufficiently large odd integer N■1 (mod 6),the equation N=p_1+p_2+p_3 has a solution in prime variables P_1,P_2,P_3 such that p_2+2=P_3,P_3+2=P_2. |
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| Keywords: | the circle method the sieve method Goldbach problem |
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