[Hint: Express a number as integral combination of powers of 10, and reduce modulo 3.] Proof. We can express a uniquely as a linear combination of powers of 10: a = a 0 + a 1 10 + a 2 102 + + a ‘ 10‘; with a ‘ 6= 0 : So since 10 3 1, we have 10k 3 1k = 1 for all k. So a 3 a 0 + a 1 1 + a 2 1 + + a ‘ 1 = a 0 + a 1 + a 2 + + a ‘: (c)The ... Jul 13, 2019 · Another way is the Euclidean Algorithm. This is much more efficient and the time complexity of this algorithm is roughly O(log_2n). This algorithm is based on the fact that when a = bq + r, then we can say that gcd(a, b) = gcd(b, r). We know from the division algorithm, a = bq + r, where r is the remainder when a is divided by b. So, r = a \mod b.

Apr 09, 2014 · Express GCD (252, 198) = 18 as a linear combination of 252 and 198 252 = 1*198 + 54 198= 3*54 + 36 54 = 1*36 + 18 36 = 2 * 18 restating... 18=54 - 1 *36 36 = 198 - 3 * 54 So we just rearranged the... Sep 12, 2018 · I imagine math software would use this algorithm to compute it as subtractions are relatively cheap compared to multiplications or divisions. Another remote possibility is it uses a combination of lookup table and Euclidean algorithm to speed things up although that may take up more memory than necessary and depending on the table size more ...

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