Weak Schur number $WS(9)$
The largest number $n$ such that the integers $1$ to $n$ can be colored with $9$ colors with no monochromatic solution to $x + y = z$ with $x \neq y$.
Lower bound:
$22536$
(22,536)
Upper bound:
Unknown
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
- Lower bound: None yet
- Upper bound: None yet
Updates from the literature
-
2017
Lower bound: $15596$
(15,596)
F. Rafilipojaona, Lower bounds on the weak Schur numbers up to 9 colors, Integers 17 (2017) #A39.
[via R. Ageron, P. Casteras, T. Pellerin, Y. Portella, A. Rimmel and J. Tomasik, New lower bounds for Schur and weak Schur numbers, arXiv:2112.03175.] -
2020-11-23
Lower bound: $21848$
(21,848)
F. Rowley, New lower bounds for weak Schur partitions, Integers 21 (2021) #A59, arXiv:2011.11292.
[via R. Ageron, P. Casteras, T. Pellerin, Y. Portella, A. Rimmel and J. Tomasik, New lower bounds for Schur and weak Schur numbers, arXiv:2112.03175.] -
2021-12-06
Lower bound: $22536$
(22,536)
R. Ageron, P. Casteras, T. Pellerin, Y. Portella, A. Rimmel and J. Tomasik, New lower bounds for Schur and weak Schur numbers, arXiv:2112.03175.