# squarefull number

A natural number $n$ is called squarefull (or powerful) if for every prime $p|n$ we have $p^{2}|n$. In 1978 Erdős conjectured that we cannot have three consecutive squarefull natural numbers. If we assume the ABC Conjecture, there are only finitely many such consecutive triples.

 Title squarefull number Canonical name SquarefullNumber Date of creation 2013-03-22 11:45:26 Last modified on 2013-03-22 11:45:26 Owner KimJ (5) Last modified by KimJ (5) Numerical id 10 Author KimJ (5) Entry type Definition Classification msc 11A51 Classification msc 55-00 Classification msc 82-00 Classification msc 83-00 Classification msc 81-00 Classification msc 39A99 Classification msc 39B72 Classification msc 33E30 Synonym powerful number Related topic NFullNumber