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squarefull number (Definition)

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




"squarefull number" is owned by KimJ.
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See Also: $n$-full number

Other names:  powerful number
Keywords:  number theory
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Cross-references: ABC conjecture, consecutive, prime, natural number
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This is version 5 of squarefull number, born on 2001-10-15, modified 2005-03-10.
Object id is 204, canonical name is SquarefullNumber.
Accessed 4676 times total.

Classification:
AMS MSC11A51 (Number theory :: Elementary number theory :: Factorization; primality)

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