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How many times does n go into n ǃ

Published online by Cambridge University Press:  01 August 2016

Nick MacKinnon
Nick MacKinnon*
Affiliation:
Winchester College
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Extract

Sometimes nǃ is very divisible by n. For example, 12ǃ is divisible by 125 while 720ǃ is divisible by 720178. On the other hand, if p is prime then pǃ is divisible by p but not by p2.

In general it is quite difficult to calculate the maximum exponent m(n) such that nm(n) divides nǃ

In this short article I will locate some values of n, for which nǃ is very divisible by n, find a tight upper bound for m(n), and point the reader in the direction of related problems.

Type
Research Article
Information
The Mathematical Gazette , Volume 70 , Issue 453 , October 1986 , pp. 203 - 205
Copyright
Copyright © The Mathematical Association 1986

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