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.)

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 [BBC24] proved that there are infinitely many four-term arithmetic progressions of pairwise coprime powerful numbers. (Without coprimality this is easy, and by a theorem of Fermat there are no four *squares* in arithmetic progression.)