Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647308 | Discrete Mathematics | 2015 | 5 Pages |
Abstract
For a given positive integer N, and any coloring function c:Nâ{0,1} satisfying c(2k)=1âc(k), c(2k+1)=c(k) for all kâ¥N, we show that for all nâ¥20N, n has both a monochromatic representation and a multicolored representation, in other words, there exist x,y,u,vâN, such that n=x+y=u+v, c(x)=c(y) and c(u)â c(v). Similar results are obtained for another kind of coloring function c:Nâ{0,1} satisfying c(2k)=c(k) and c(2k+1)=1âc(k) for all kâ¥N. This answers a question of Y.-G. Chen on the values of representation functions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Zhenhua Qu,