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exactly divides (Definition)

Let $ p$ be a prime, $ m$ be a positive integer, and $ n$ be an integer. Then $ p^m$ exactly divides $ n$ (denoted as $ p^m \Vert n$) if $ p^m$ divides $ n$ and $ p^{m+1}$ does not divide $ n$.



"exactly divides" is owned by Wkbj79.
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See Also: divides, divisibility, strict divisibility
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Cross-references: divides, integer, positive, prime
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This is version 2 of exactly divides, born on 2006-08-20, modified 2006-08-20.
Object id is 8266, canonical name is ExactlyDivides.
Accessed 866 times total.

Classification:
AMS MSC: 11A51 (Number theory :: Elementary number theory :: Factorization; primality)
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