... r3. We continue in this way, each time dividing the last remainder into the second-to-last remainder, obtaining a new quotient and remainder. When we finally obtain a remainder that divides ... that a2 must always be replaced by a + 1, since a satisfies X2 = X + 1): a& apos; = a, a2 = a + 1, a3 = -a + 1, a4 = -1 , a5 = a, a6 = -a - 1, a7 = a - 1, ... b 2a3 , then any element blai' in blS is of the form to - be in b2S, because blail = bla'ai&apos ;-& apos; - b2aj+" ;-& apos; ). And each coset contains exactly d elements. Since...