The Extended Euclidean Algorithm is used to compute gcd of r0 and r1 in the form: gcd(r0, r1) = sr0 + t r1 Assume r0, r1, s, t in Z Show that if gcd(r0, r1) = 1, then r1 has a multiplicative inverse in mod (r0). What is the inverse? Starting from the above equation, prove that a multiplicative inverse exists for r1 in mod(r0). Also give an expression for the inverse.

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