Question

If c > 0, prove that (ca,cb) =c(a,b).

Answer 1

well geometrically speaking if (a,b) is a point and we multiply it by c ,then both a and b will get multiplied by c. lets see if i can provide an algebraic proof

Answer 2

i think (a,b) represents the GCD

Answer 3

Let a=nx and b=ny where n is the GCD of a and b then,
ca=c*a=c*n*x [ NOTE c>0]
cb=c*b=c*n*y
Thus, (ca,cb)=cn
ALSO, c(a,b)=c*n=cn
Thus,
If c > 0, (ca,cb) =c(a,b)

Answer 4

Thank you for your help today.

Answer 5

welcome