For A Zm and n ∈ Zm, let σA(n) be the number of solutions of equation n =x + y, x, y ∈ A. Given a positive integer m, let Rm be the least positive integer r such that there exists a set A Zm with A + A = Zm ...For A Zm and n ∈ Zm, let σA(n) be the number of solutions of equation n =x + y, x, y ∈ A. Given a positive integer m, let Rm be the least positive integer r such that there exists a set A Zm with A + A = Zm and σA(n) ≤ r. Recently, Chen Yonggao proved that all Rm ≤ 288. In this paper, we obtain new upper bounds of some special type Rkp2.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10901002 10771103)
文摘For A Zm and n ∈ Zm, let σA(n) be the number of solutions of equation n =x + y, x, y ∈ A. Given a positive integer m, let Rm be the least positive integer r such that there exists a set A Zm with A + A = Zm and σA(n) ≤ r. Recently, Chen Yonggao proved that all Rm ≤ 288. In this paper, we obtain new upper bounds of some special type Rkp2.