The Euclidean Algorithm - luc.edu

Proof. By the lemma, we have that at each stage of the Euclidean algorithm, gcd(r j;r j+1) = gcd(r j+1;r j+2). The process in the Euclidean algorithm produces a strictly decreasing sequence of remainders r 0 > r 1 > r 2 > > r n+1 = 0. This sequence must terminate with … ................
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