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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 $n_k,n_{k+1},n_{k+2}$?
#938
:
[Er76d]
number theory
Erdős also conjectured (see
[364]
) that there are no triples of powerful numbers of the shape $n,n+1,n+2$.
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