Math Is Fun Forum

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Integer Factorisation

Prove the following:
If:

where p are prime numbers
Then:

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'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.

scientia

Member

Registered: 2009-11-13

Posts: 224

Re: Integer Factorisation

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,648

Re: Integer Factorisation

hi scientia

Nice proof! 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

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'
I'm not crazy, my mother had me tested.