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Let be maximal such that there exists, for all , a congruence class such that every satisfies at least of these congruences.
Estimate .
Source: erdosproblems.com/1205
A full solution has been claimed but not yet accepted. Settled in another form, for example when its parts resolve differently or the question is open-ended.
SOLVED, the site's label, which the page glosses as a resolution by
some means other than a proof or disproof: the site's own commentary gives an
argument that , with the two-sided bound
. The status-defining
source is that commentary (last edited 8 April 2026), which this compilation
admits as a source for status. No paper, preprint or independent review of the
argument exists, and the label is the claimant's own (the site's curator, T. F.
Bloom, wrote the argument, so the curator's label is no independent review), so
the argument is a pending claim
(the site's argument, April 2026)
and the derived standing is claimed, not solved. The argument is presented
below as the site's account with its steps named and is not checked step by step
here.