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  3. 4. (a) use the euclidean algorithm to find the gre

4. (a) Use the Euclidean algorithm to find the greatest common divisor of 21 and 13,...

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Advance Math

4. (a) Use the Euclidean algorithm to find the greatest commondivisor of 21 and 13, and the greatest common divisor of 34 and21.

(b) It turns out that 21 and 13 is the smallest pair of numbersfor which the Euclidean algorithm requires 6 steps (for every otherpair a and b requiring 6 or more steps a > 21 and b > 13).Given this, what can you say about 34 and 21?

(c) Can you guess the smallest pair of numbers requiring 8Euclidean algorithm steps?

(d) Is there a pattern here? Do the numbers which keep coming uphave a name?

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