Erdős Problem #721
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
A nonconstant arithmetic progression of length `n` and color `b` in `[1,N]`. Only positive lengths are used in the research targets.
Every coloring has either a red three-term or a blue `k`-term progression. Here `false` denotes red and `true` denotes blue.
An eventual upper bound by `exp(k^c)`, for one fixed exponent `0 < c < 1`. Existence of a forcing interval is included explicitly.
Attempts
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