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

Agnishom wrote:

Prove the following:

If:

where p aredistinctprime 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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,315

hi scientia

Nice proof!

Bob

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

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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

**Online**

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