- Also, if a=b=d, gcd(a,b)=d, but gcd(0,d)=0.

Jon Perry

perry@...

http://www.users.globalnet.co.uk/~perry

http://www.users.globalnet.co.uk/~perry/maths

BrainBench MVP for HTML and JavaScript

http://www.brainbench.com

-----Original Message-----

From: Phil Carmody [mailto:fatphil@...]

Sent: 08 January 2002 11:09

To: primenumbers@yahoogroups.com

Subject: Re: [PrimeNumbers] New primers

On Tue, 08 January 2002, "paulmillscv" wrote:

> Prove that if gcd(a,b) = d, then gcd( |a-b|,min(a,b)) = d. where

> || is the modulus function, and min(a,b) is the min function.

That's a bit noisy - gcd is symmetric, so gcd(a,b)=gcd(b,a). Therefore you

can simply assume WLOG[*] a>=b, and your expression becomes, with no need

for abs or min,

gcd(a,b)=d -> gcd(a-b, b)=d

The proof is almost not deserving of the word, as

d|a & d|b -> d|(a-b),

d|(a-b) & d|b -> d|a

Phil

[* WLOG = Without Loss Of Generality]

Don't be fooled, CRC Press are _not_ the good guys.

They've taken Wolfram's money - _don't_ give them yours.

http://mathworld.wolfram.com/erics_commentary.html

Find the best deals on the web at AltaVista Shopping!

http://www.shopping.altavista.com

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com

The Prime Pages : http://www.primepages.org

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/ - Reminds me of the riddle:

What is apple multiplied by car?

Jon Perry

perry@...

http://www.users.globalnet.co.uk/~perry

http://www.users.globalnet.co.uk/~perry/maths

BrainBench MVP for HTML and JavaScript

http://www.brainbench.com

-----Original Message-----

From: Michael Bell [mailto:mike.d.bell@...]

Sent: 08 January 2002 20:24

To: Primes List

Subject: Re: [PrimeNumbers] New primers

0/0 shouldn't be defined as zero, consider the following:

What is x/x as x-->0? What is (x*x)/x as x-->0? What is x/(x*x) as x-->0?

This clearly shows that 0/0 can take the values 0, 1 and infinity, and

indeed cna be made to tak any value you care to name. So "undefined" is

definitely the best thing for it.

Michael.

> I think 0/0 should be defined as 0. 0 multiplied by any non-zero number

my

> gives 0, and I don't see why multiplying it by infinity should be any

> different.

>

> If this is not so, then I could take my zero Euro's, and divide them into

> zero people, and end up extremely wealthy.

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com

>

> Jon Perry

The Prime Pages : http://www.primepages.org

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/