What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.14
(Solved) Define the 2-colour van der Waerden numbers $W(k, r)$ to be the least quantities such that if $\{1, ..., W(k, r)\}$ is coloured red and blue then there is either a red $k$-term progression or a blue $r$-term progression. Is $W(k, r)$ a polynomial in $r$, for fixed $k$? Is $W(3, r) ≪ r^2$?
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What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.14
(Solved) Define the 2-colour van der Waerden numbers$W(k, r)$ to be the least quantities such that if $\{1, ..., W(k, r)\}$ is coloured red and blue then there is either a red $k$ -term progression or a blue $r$ -term progression. Is $W(k, r)$ a polynomial in $r$ , for fixed $k$ ? Is $W(3, r) ≪ r^2$ ?
AMS categories
Choose either option