Weak Schur number $WS(8)$

The largest number $n$ such that the integers $1$ to $n$ can be colored with $8$ colors with no monochromatic solution to $x + y = z$ with $x \neq y$.

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

• 2015-09-17 Lower bound: $5105$
  B. Bouzy, An Abstract Procedure to Compute Weak Schur Number Lower Bounds, LIPADE technical report TR-2 (2015).
  [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.]
• 2017 Lower bound: $5201$
  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: $6976$
  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.]