squarefull number SquarefullNumber 2001-10-15 20:07:55 2005-03-10 07:48:55 Definition number theory \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} A natural number $n$ is called squarefull (or powerful) if for every prime $p | n$ we have $p^2 | n$. In 1978 Erd\H{o}s conjectured that we cannot have three consecutive squarefull natural numbers. If we assume the ABC Conjecture, there are only finitely many such consecutive triples.