Thread: (a;b)=(a;a+b)

Hi!
I have such task:

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!

What have you been studying in class?

On its own your assignment is meaningless.

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.

a and b are natural numbers, I suppose.
And those brackets mean the greatest common divisor of the numbers inside.

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.