| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4656272 | Journal of Combinatorial Theory, Series A | 2008 | 9 Pages |
Abstract
For positive integers a1,a2,…,am, we determine the least positive integer R(a1,…,am) such that for every 2-coloring of the set [1,n]={1,…,n} with n⩾R(a1,…,am) there exists a monochromatic solution to the equation a1x1+⋯+amxm=x0 with x0,…,xm∈[1,n]. The precise value of R(a1,…,am) is shown to be av2+v−a, where a=min{a1,…,am} and . This confirms a conjecture of B. Hopkins and D. Schaal.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
