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Unformatted text preview: show something simpler. Lemma: If a >= b then gd (a,b) = gcd(a - b, b). Proof: Any number that divides a and b also divides a b mod b. any number that divides a-b mod b also divides a and b. therefore, (a,b) and (a-b,b) have the same divisors, therefore, same GCD. Gcd (550, 121) = gcd (550 mod 121, 121) = gcd (121, 66) = gcd (55, 11) = gcd (11, 0) Gcd(231, 60) = gcd(51, 9) = gcd(9, 6) = gcd(6,3) = 3. E. How fast is it: Lemma: if a >=b then a mod b < a/2. Case(i) b <= a/2 case 2: b > a/2. . F....
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- Spring '08