Transcribed Image Text: Let ro, r1, r2, . .. (where ro = b) be the successive remainders in the Euclidean algorithm applied to find gcd(a,
Transcribed Image Text: Let ro, r1, r2, . .. (where ro = b) be the successive remainders in the Euclidean algorithm applied to
find gcd(a, b).
(a) Show that every two steps reduces the remainder by at least one half. In other words, show that
1
for every i = 0, 1, 2, …
Ti+2 <
(b) Show that the Euclidean algorithm will terminate in at most 2 log2 (b) steps. In particular, the
number of steps is at most 6.65 times the number of digits in b.
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