典型文献
On a Problem of Q.H.YANG and Y.G.CHEN
文献摘要：
For any positive integers k1,k2 and any set A C N,let Rk1,k2(A,n)be the number of solutions of the equation n=k1a1+k2a2 with al,a2 ∈ A.Let(A)=N\A.Yang and Chen proved that if k1 and k2 are two integers with k2＞k1≥2 and(k1,k2)=1,then there does not exist any set A(∈)N such that Rk1,k2(A,n)=Rk1,k2((A),n)for all sufficiently large integers n.For two integers k＞1 and t≥1,define fk(t)to be the number of sets A(∈)N such that Ri,k(A,n)=Ri,k((A),n)holds for all integers n≥t.Yang and Chen proved that fk(t)is finite and limt→∞ log fk(t)/t=log 2.They also asked if it is true that for any integers k,l≥1 there exists to(k,l)such that fk(t)=fl(t)for all integers t≥to.In this paper,we give the exact formula of fk(t)when t≤k,which implies that fk(t)=fl(t)for all integers t≤min{k,l}.
文献关键词：
中图分类号：
作者姓名：
Xiaohui YAN
作者机构：
School of Mathematics and Statistics,Anhui Normal University,Anhui 241002,P.R.China
文献出处：
引用格式：
[1]Xiaohui YAN-.On a Problem of Q.H.YANG and Y.G.CHEN)[J].数学研究及应用,2022(06):580-586
A类：
k1a1+k2a2,limt
B类：
On,Problem,YANG,CHEN,For,any,positive,integers,let,Rk1,number,solutions,equation,Let,Yang,Chen,proved,that,if,are,two,then,there,does,not,such,all,sufficiently,large,define,fk,sets,Ri,holds,finite,log,They,also,asked,true,exists,fl,In,this,paper,we,give,exact,formula,when,which,implies
AB值：
0.387461
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