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#1 2012-10-14 16:58:02

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,229
Website

Integer Factorisation

Prove the following:
If:


where p are prime numbers
Then:


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#2 2012-10-14 21:54:41

scientia
Member
Registered: 2009-11-13
Posts: 222

Re: Integer Factorisation

Agnishom wrote:

Prove the following:
If:


where p are distinct prime numbers
Then:


Let
denote the number of positive factors of
.

It's obvious that if

and
have no factor in common other than ±1, then
.

Also the factors of

are
and so
.

Combining the two observations above gives the required solution.

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#3 2012-10-14 22:29:19

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: Integer Factorisation

hi scientia

Nice proof!  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#4 2012-10-14 23:05:15

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,229
Website

Re: Integer Factorisation

Thanks @scientia


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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