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| Chen’s Conjecture and Its Generalization |
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Citation： |
Xuegong SUN,Lixia DAI.Chen’s Conjecture and Its Generalization[J].Chinese Annals of Mathematics B,2013,34(6):957~962 |
| Page view： 1601
Net amount： 1136 |
Authors： |
Xuegong SUN; Lixia DAI; |
Foundation： |
National Natural Science Foundation of China (Nos. 10771103, 10801075) andthe Natural Science Foundation of Huaihai Institute of Technology (No.KQ10002). |
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| Abstract： |
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 2n + pα is at least c(g)x, where
p is an odd prime and the constant c(g) depends only on g. |
Keywords： |
Chen’s conjecture, Powers of 2, Primes, Selberg’s sieve method |
Classification： |
11A07, 11B25, 11P32 |
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