Chen's Conjecture and Its Generalization

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+pαis at least c（g）x,where p is an odd prime and the constant c（g）depends only on g.