一类加法补集问题的研究

On a problem of additive complements

对于加法补集A={∑∈_ia^(2i),∈i=0,1,…,a-1},,B={∑∈_ja^(2j-1)∈,j=0,1,…,a-1},当a=2时给出了满足A(x)B(x)-x=1的所有正整数x,改进了已有结果.

For additive complements A={∑∈ia^2i,∈i=0,1,…,a-1},,B={∑∈ja^2j-1∈,j=0,1,…,a-1}, all x such that A（x）B（x）-x= 1 are given when a=2, which improve the previous results.