# Math Help - Prove this function equation

1. ## Prove this function equation

This is how & works:
&(19, 14) = (5, 0) and &(12, 15) = (0, 3)

How do I show &^2 = &

2. Originally Posted by jzellt
This is how & works:
&(19, 14) = (5, 0) and &(12, 15) = (0, 3)

How do I show &^2 = &
I'm going to guess that the general form of this is: &(a,b)=(a-b,0) (when a>b) and &(a,b)=(0,b-a) (when b>a). &^2 doesn't make sense to me since & is being defined as an operation on two numbers a,b and means nothing by itself thus can't be squared. Can you explain more please?

3. Originally Posted by Jameson
I'm going to guess that the general form of this is: &(a,b)=(a-b,0) (when a>b) and &(a,b)=(0,b-a) (when b>a). [snip]
Nice guess!

To show && = & I think you would want to show that &&(a,b) = &(&(a,b)) = &(a,b). Given the above good work in defining &(a,b), it is trivial to do this ....