Permanent problem IDPPL 042
Additive combinatorics
Let the van der Waerden number W(k) be such that whenever N≥ W(k) and {1,…,N} is 2-coloured there must exist a monochromatic k-term arithmetic progression. Improve the bounds for W(k) - for example, prove that W(k)^(1/k)→ ∈fty.
Let the van der Waerden number W(k) be such that whenever N≥ W(k) and {1,…,N} is 2-coloured there must exist a monochromatic k-term arithmetic progression. Improve the bounds for W(k) - for example, prove that W(k)^(1/k)→ ∈fty.
A solution must appear in a reputable journal, with documentation that Erdős offered the displayed amount. Claims are administered by the Combinatorics Foundation; erdosproblems.com does not pay awards.