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.
We say that \(N\) is powerful if whenever \(p\mid N\) we also have \(p^2\mid N\). Let \(k\geq 3\). Can the product of any \(k\) consecutive positive integers ever be powerful?
Do all pairs of consecutive powerful numbers \(n\) and \(n+1\) come from solutions to Pell equations? In other words, must either \(n\) or \(n+1\) be a square? The answer to the first question is no: Golomb [Go70] observed that both…
Let \(B_2(n)\) be the \(2\)-full part of \(n\) (that is, \(B_2(n)=n/n'\) where \(n'\) is the product of all primes that divide \(n\) exactly once). Is it true that, for every fixed \(k \geq 1\),…
Are there infinitely many four-term arithmetic progressions of coprime powerful numbers? (A number \(n\) is *powerful* if \(p \mid n \to p^2 \mid n\); Nat.Powerful.) Erdős [Er76d] asked this; the answer is **yes**: Bajpai, Bennett and Chan…
Let \(A=\{n_1 < n_2 < \cdots\}\) be the sequence of powerful numbers (if \(p\mid n\) then \(p^2\mid n\)). Are there only finitely many three-term progressions of consecutive terms \(n_k,n_{k+1},n_{k+2}\)?
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.