Euclid’s Algorithm for computing the gcd of two numbers, r0 and r1

r0 = q1 r1 + r2

r1 = q2 r2 + r3

r2 = q3 r3 + r4

……

rm-2 = qm-1 rm-1 + rm

rm-1 = qm rm

gcd(r0, r1) = gcd(r1, r2) = … = gcd (rm-1, rm) = rm

To determine if b < n has a multiplicative inverse modulo n, start with r0 = n and r1 = b

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