Problem Statement
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 $n_k,n_{k+1},n_{k+2}$?
Are there only finitely many three-term progressions of consecutive terms $n_k,n_{k+1},n_{k+2}$?
Categories:
Number Theory Powerful
Progress
Erdős also conjectured (see [364]) that there are no triples of powerful numbers of the shape $n,n+1,n+2$.Source: erdosproblems.com/938 | Last verified: January 19, 2026