Problem 937

Are there infinitely many four-term arithmetic progressions of coprime powerful numbers (i.e. if $p\mid n$ then $p^2\mid n$ )?

Status

SolvedProved

An accepted solution exists. The statement is true.

PROVED (LEAN).

BBC24: Bajpai, Prajeet and Bennett, Michael A. and Chan, Tsz Ho, Arithmetic progressions in squarefull numbers. Int. J. Number Theory 20 (2024), no. 1, 19-45. DOI: 10.1142/S1793042124500027.
BW24: Bennett, Michael A. and Walsh, P. G., Computing four-term arithmetic progressions of powerful numbers. INTEGERS 24A (2024), A3. DOI: 10.5281/zenodo.11352598.
Er76d: Erdős, P., Problems and results on number theoretic properties of consecutive integers and related questions. Proceedings of the Fifth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1975) (1976), 25-44.