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### Re^2: A bad shuffle

by tlm (Prior)
 on Mar 24, 2005 at 00:45 UTC ( #441930=note: print w/replies, xml ) Need Help??

in reply to Re: A bad shuffle

NN-1/(N-1)! is not an integer for any integer N > 2, so it is not the case that N! | NN, except for N=1 and N=2.

the lowliest monk

Update: Here's a proof of the assertion made above. I'm sure there are better proofs of it, but this is the best I could come up with.

Assume that N > 2, and let p be the largest prime in the prime factorization of N. There are three cases to consider. Suppose first that p is 2. Then, by assumption, N is a power of 2 greater than or equal to 4. Therefore, 3 is a factor of N!, and consequently N! does not divide NN. Next, suppose that p > 2. If N = pk for some nonnegative integer k, then N is odd and not divisible by N! whose prime factorization includes 2. This leaves the case in which p > 2, and is not the sole prime factor of N. In this case N >= 2 p. By Bertrand's postulate there exists a prime q such that p < q < 2 p <= N. Therefore, there is a factor of N!, namely q, that does not divide Ns, for any positive integer s. Therefore, N! does not divide NN, for all N > 2.

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 [moritz]: choroba in python I use jsonschema [moritz]: I'm sure there's a Perl implementation of it too [choroba]: it seems Kelp and similar help you a lot with dispatching, but how to do something similar with contents? [moritz]: like JSON::Schema [Corion]: ambrus++ # more bugs than lines [Corion]: That's like "works on my machine" ;-) [choroba]: I mean, I'd like to say "this path should run this sub, but first it should check the user is authenticated, has the following permissions, and the contents is valid against a given schema [ambrus]: no, that means I haven't even tried to run it, might not even parse [ambrus]: so it doesn't work on my machine [choroba]: i.e. I know JSON::Schema, I'm just curious whether there's a ready solution to plug it into a web service

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