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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,127
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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'
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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: 6,420

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: 17,127
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'
'You made a human being happy! There is no further achievement.' -bobbym

Online

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