The Euclidean Algorithm and Multiplicative Inverses
Theorem 2 (Multiplicative Inverse Algorithm). Given two integers 0 < b < a, consider the Euclidean Algorithm equations which yield gcd(a,b) = rj. Rewrite all of these equations ... so that (the residue of) y is the multiplicative inverse of b, mod a. Examples! Example 2. Find integers x and y to satisfy 42823x +6409y = 17.
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