Regenerated from the community database (Apache-2.0), dated, and linked back to it
from every problem. erdosproblems.com no longer shows statuses (Bloom's reasons); this is the database's record, not our verdict.
908 of 1221 statements are formalized in Lean (Formal Conjectures) · 107 carry an Erdős prize · 3 are independent of ZFC and 9 more can't be proved, or can't be disproved, from ZFC alone · “open” counts the computable and Lean-checked ones too.
Let \(k\geq 3\) and \(A\subset \mathbb{N}\) be the set of \(k\)th powers. What is the order of growth of \(1_A^{(k)}(n)\), i.e. the number of representations of \(n\) as the sum of \(k\) many \(k\)th powers? Does there exist some \(c>0\)…
Is it true that \(f_{k,k}(x) \gg_\epsilon x^{1-\epsilon}\) for all \(\epsilon>0\)? This would have significant applications to Waring's problem. Erdős and Graham describe this as 'unattackable by the methods at our disposal'.
Writing \(f_{k, 3}(x)\) for the number of integers \(\leq x\) which are the sum of three \(k\)th powers, is it true that \(f_{k, 3}(x) \gg x ^ (3 / k)\)?
Source: teorth/erdosproblems (its own interactive table), Apache-2.0, pulled 2026-10-21. A status here is what that database records, not an independent verification by us, except where a problem page says so.