What is the fifth weak Schur number?

TheoremDB P11256 · combinatorics

Inferred from the community field; finer classification has not been reviewed.

Source catalogue assessmentAs of 2026-09-08Source & evidence ↓

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Problem statement

Let $WS(r)$ be the largest m for which the integers 1 through m can be colored with r colors so that no three distinct integers a,b,c of one color satisfy a+b=c. What is WS(5)?

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Background

Additional formulation recorded by the source

WS(5)=\max{m:\exists\chi:[m]\to[5]\ \forall 1\le a<b,\ a+b\le m\Rightarrow \neg(\chi(a)=\chi(b)=\chi(a+b))}.\quad \text{Determine }WS(5).

Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

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References

[1]TheoremDB P11256 link

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