Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

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'

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

**Online**

**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.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,420

hi scientia

Nice proof!

Bob

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

**Online**

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**

Pages: **1**