Baudet's Conjecture

If C_1, C_2, ...C_r are sets of positive integers and

  union _(i=1)^rC_i=Z^+,

then some C_i contains arbitrarily long arithmetic progressions. The conjecture was proved by van der Waerden (1927) and is now known as van der Waerden's Theorem.

According to de Bruijn (1977), "We do not know when and in what context he [Baudet] stated his conjecture and what partial results he had," although van der Waerden (1971, 1998) indicates he first heard of the problem in 1926.

See also

Arithmetic Progression, van der Waerden's Theorem

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de Bruijn, N. G. "Commentary." Unpublished manuscript, pp. 116-124, 1977. der Waerden, B. L. "Beweis einer Baudetschen Vermutung." Nieuw Arch. Wisk. 15, 212-216, 1927.van der Waerden, B. L. "How the Proof of Baudet's Conjecture Was Found." Studies in Pure Mathematics (Presented to Richard Rado). London: Academic Press, pp. 251-260, 1971.van der Waerden, B. L. "Wie der Beweis der Vermutung von Baudet gefunden wurde." Elem. Math. 53, 139-148, 1998.

Cite this as:

Weisstein, Eric W. "Baudet's Conjecture." From MathWorld--A Wolfram Web Resource.

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