A conjecture of Erdös on 3-powerful numbers
Abstract: Erdös conjectured that the Diophantine equation has infinitely many solutions in pairwise coprime 3-powerful integers, i.e., positive integers for which implies . This was recently proved by Nitaj who, however, was unable to verify the further conjecture that this could be done infinitely often with integers , and none of which is a perfect cube. This is now demonstrated.
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J. H. E. Cohn
Affiliation: Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom
Received by editor(s): May 15, 1996
Received by editor(s) in revised form: September 13, 1996
Article copyright: © Copyright 1998 American Mathematical Society