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

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

(b) It turns out that 21 and 13 is the smallest pair of numbers for which the Euclidean algorithm requires 6 steps (for every other pair 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 8 Euclidean algorithm steps?

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

Expert Solution

Colby Messinger answered 2 years ago

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