Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9505797 | Advances in Applied Mathematics | 2005 | 9 Pages |
Abstract
For all integers m⩾3 and all natural numbers a1,a2,â¦,amâ1, let n=R(a1,a2,â¦,amâ1) represent the least integer such that for every 2-coloring of the set {1,2,â¦,n} there exists a monochromatic solution to a1x1+a2x2+â¯+amâ1xmâ1=xm. Let t=min{a1,a2,â¦,amâ1} and b=a1+a2+â¯+amâ1ât. In this paper it is shown that whenever t=2, R(a1,a2,â¦,amâ1)=2b2+9b+8. It is also shown that for all values of t, R(a1,a2,â¦,amâ1)⩾tb2+(2t2+1)b+t3.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Brian Hopkins, Daniel Schaal,