> In normal arithmetic of course, multiplication and division aren't reversible because of zero. If a and b are in the range 0-255, am I right in thinking that

> In normal arithmetic of course, multiplication and division aren't reversible because of zero. If a and b are in the range 0-255, am I right in thinking that (((a + 1) * (b + 1)) % 257) - 1 is also in the range 0-255? Does that also work as a group operation? Does division done this way have the properties you'd need?