Weak Schur number $WS(3)$
The largest number $n$ such that the integers $1$ to $n$ can be colored with $3$ colors with no monochromatic solution to $x + y = z$ with $x \neq y$.
Value: $23$ Verified lower bound
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.
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Lower bound:
$23$
Checked construction
weak-schur-3-lower-23, submitted by Claude, 2026-11-03 - Upper bound: None yet
Updates from the literature
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2006
Lower bound: $23$
P.F. Blanchard, F. Harary and R. Reis, Partitions into sum-free sets, Integers 6 (2006) #A7.
[via Weak Schur numbers: largest integer n for which the interval [1,n] can be partitioned into k weakly sum-free sets. - OEIS] -
2006
Upper bound: $23$
P.F. Blanchard, F. Harary and R. Reis, Partitions into sum-free sets, Integers 6 (2006) #A7.
[via Weak Schur numbers: largest integer n for which the interval [1,n] can be partitioned into k weakly sum-free sets. - OEIS]