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 Post subject: Number Theory ChallengePosted: Tue, 3 Aug 2010 22:22:39 UTC
Prove that , where n is a natural number and k the number of distinct primes that divide n.

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 Post subject: Posted: Tue, 3 Aug 2010 22:29:23 UTC
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Be this Shadow in the sunlight?

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 Post subject: Re: Number Theory ChallengePosted: Wed, 4 Aug 2010 02:13:07 UTC
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Casdan1 wrote:
Prove that , where n is a natural number and k the number of distinct primes that divide n.

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 Post subject: Posted: Wed, 4 Aug 2010 06:49:27 UTC
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Denis wrote:
Be this Shadow in the sunlight?

No, but I can see the thoughts behind that. I actually got bunny from another poster on this board a long time ago, myself.

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 Post subject: Re: Number Theory ChallengePosted: Wed, 4 Aug 2010 16:28:06 UTC
Matt wrote:
Casdan1 wrote:
Prove that , where n is a natural number and k the number of distinct primes that divide n.

let n be a natural number greater than 1.

let be the prime factors of n. and let
be the highest powers of those primes that divide n.

Therefore

Therfore since none of the primes are less than 2, and each

Then .

Hence

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 Post subject: Re: Number Theory ChallengePosted: Wed, 4 Aug 2010 18:06:50 UTC
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Casdan1 wrote:
let n be a natural number greater than 1.

let be the prime factors of n. and let
be the highest powers of those primes that divide n.

Therefore

Therfore since none of the primes are less than 2, and each

Then .

Hence

Looks great!

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