Question: 3. [a] Use the Euclidean algorithm to nd the greatest common divisor of 21 and 13: and the greatest common divisor of 34 and 21.

3. [a] Use the Euclidean algorithm to nd 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 5 steps [for every other pair a and b requiring 5 or more steps a 3 21 and b 9 13). Given thisI 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

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