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Schur's Ramsey Theorem

As shown by Schur (1916), the Schur number S(n) satisfies

S(n)<=R(n)-2

for n=1, 2, ..., where R(n) is a Ramsey number.

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References

Fredricksen, H. and Sweet, M. M. "Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers." Electronic J. Combinatorics 7, No. 1, R32, 1-9, 2000. http://www.combinatorics.org/Volume_7/Abstracts/v7i1r32.html.Schur, I. "Über die Kongruenz x^m+y^m=z^m mod p." Jahresber. Deutsche Math.-Verein. 25, 114-116, 1916.

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Schur's Ramsey Theorem

Cite this as:

Weisstein, Eric W. "Schur's Ramsey Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchursRamseyTheorem.html

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