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#1 2015-10-24 07:11:48

zetafunc
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Analytic Number Theory

It would be worthwhile to read this thread first, for the definitions of the terms and functions used in these exercises.

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#2 2015-10-24 07:13:03

zetafunc
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Re: Analytic Number Theory

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#3 2015-10-24 07:24:25

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Re: Analytic Number Theory

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#4 2015-10-24 07:30:31

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Re: Analytic Number Theory

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#5 2015-10-24 07:37:19

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#6 2015-10-24 07:43:02

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Re: Analytic Number Theory

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#7 2015-10-24 07:44:02

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Re: Analytic Number Theory

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#8 2015-10-25 04:11:03

Agnishom
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Re: Analytic Number Theory

zetafunc wrote:

It would be worthwhile to read this thread first, for the definitions of the terms and functions used in these exercises.

#1

Not true.

Mobius(4) != Mobius(2)*Mobius(2)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#9 2015-10-25 04:35:41

Agnishom
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Re: Analytic Number Theory

zetafunc wrote:

#2

Once again, isn't that just the definition of what perfect numbers are?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#10 2015-10-25 05:01:05

zetafunc
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Re: Analytic Number Theory

Agnishom wrote:

Not true.

Mobius(4) != Mobius(2)*Mobius(2)

That is not a counter-example. 2 is not coprime to itself: all you have shown is that it is not totally multiplicative.

Last edited by zetafunc (2015-10-25 05:04:30)

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#11 2015-10-25 05:04:12

zetafunc
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Re: Analytic Number Theory

Agnishom wrote:

Once again, isn't that just the definition of what perfect numbers are?

Yes, but perhaps the question ought to have been phrased in terms of a more elementary definition of the perfect numbers, such as: "Given that a perfect number is a number which is equal to the sum of its proper divisors, explain why this is equivalent to   

Last edited by zetafunc (2015-10-25 05:13:47)

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#12 2015-10-27 05:58:24

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Re: Analytic Number Theory

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#13 2015-11-06 23:11:36

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#14 2015-12-19 23:56:52

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#15 2015-12-29 02:10:44

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#16 2015-12-29 02:14:54

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#17 2015-12-29 02:22:20

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