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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**scientia****Member**- Registered: 2009-11-13
- Posts: 224

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: 7,013

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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