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Can be -coloured such that if
is a -term monochromatic arithmetic progression then for all ?
Source: erdosproblems.com/984
An accepted solution exists. The statement is true.
Proved. The label is the site's (PROVED, page last edited 4 April 2026, read 2026-10-07), with the commentary crediting Zach Hunter's proof on the discussion thread. The standing is derived from the claim page: the accepted claim is Hunter's -coloring of 10 August 2025, on its claim page (Hunter, 2025), which gives every monochromatic -term progression starting at at most terms and is accepted on the site's label; no write-up outside the thread was found on 2026-10-07. Spencer's three-color version with a very slowly growing bound and Erdős's two-coloring with are the earlier results the site records.