2. Show that a mod b and a divb are well-defined. That is, show that if r, r' are two numbers in {0, 1, 2, ..., b-1} and k, k' ∈ Z such that a = r+k·band a = r'+k'·b, then r = r' and k = k' follow. (Hint: Use 0 = (r-r') + (k-k')·b.)