Van der Waerden number $W(5,5)$
The smallest number $n$ such that if the integers $1$ to $n$ are colored with $5$ colors, there must be a monochromatic arithmetic progression of length $5$.
Lower bound:
$98742$
(98,742)
Upper bound:
Unknown
Updates
-
2017-06-21
Lower bound: $98742$
(98,742)
Heule, M. J. (2017). Avoiding triples in arithmetic progression. Journal of Combinatorics, 8(3), 391-422.
[via Van der Waerden number - Wikipedia]