# (a;b)=(a;a+b)

• Nov 4th 2012, 04:06 AM
Kiiefers
(a;b)=(a;a+b)
Hi!

Demonstrate, that, (a;b)=(a;a+b)

There is no more explanation. Teacher said that there is somthing to do with number sharing properties.
• Nov 4th 2012, 04:29 AM
a tutor
Re: (a;b)=(a;a+b)
What have you been studying in class?

On its own your assignment is meaningless.
• Nov 4th 2012, 04:29 AM
Plato
Re: (a;b)=(a;a+b)
Quote:

Originally Posted by Kiiefers
Demonstrate, that, (a;b)=(a;a+b)
There is no more explanation. Teacher said that there is somthing to do with number sharing properties. Please help!

With so little given there is no way to help you. Sorry.
• Nov 4th 2012, 07:26 AM
Kiiefers
Re: (a;b)=(a;a+b)
a and b are natural numbers, I suppose.
And those brackets mean the greatest common divisor of the numbers inside.
• Nov 4th 2012, 10:15 AM
HallsofIvy
Re: (a;b)=(a;a+b)
And it didn't occur to you to tell us that to begin with? sigh.

If n= (a; b), the greatest common divisor of a and b, since n is a common divisor, then a= xn and b= yn. a+ b= xn+ yn= (x+y)n so that n is a common divisor of a and a+ b. Now, suppose there were a larger common divisor- that is there exist m such that a= mj, a+ b= mk for integers j and k and m> n. The b= (a+ b)- a= mk- mj= m(k- j) so that m is also a common divisor of b.