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| Chen’s Conjecture and Its Generalization | |
| 作者姓名： | Xuegong SUN Lixia DAI |
| 基金项目： | Project supported by the National Natural Science Foundation of China （Nos. 10771103, 10801075） and the Natural Science Foundation of Huaihai Institute of Technology （No. KQ10002）. Acknowledgement We sincerely thank Professor Yong-Gao Chen for his useful suggestions and effective help! |
| 摘 要： | Let l1, l2, ..., lg be even integers and x be a sufficiently large number. In this paper, the authors prove that the number of positive odd integers k ≤ x such that （k ＋l1）^2, （k ＋l2）^2, ..., （k ＋lg）^2 can not be expressed as 2^n＋p^α is at least c（g）x, where p is an odd prime and the constant c（g） depends only on g. |
| 关 键 词： | 猜想 正奇数 奇素数 LG 整数 |
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