Main Question or Discussion Point
What does the notation gcd(x,y) means?
I perfer a definition that does not require an ordering of element such asHurkyl said:It stands for greatest common divisor. It has two equivalent characterizations:
d = gcd(x, y) iff d is the largest thing such that d|x and d|y.
d = gcd(x, y) iff d is the smallest nonzero thing of the form ux + vy. (u and v need not be greater than zero)
(Size is measured by absolute value. We always use the positive one)
Note that all of this makes sense for more than just integers -- for example, it works for polynomials if "size" is measured by degree. (We always choose the monic polynomial)