Question 2: Inverse in Modular Arithmetic [5 points] Using Extended Euclidean Algorithm, find a multiplicative inverse of a in Z_m for a = 53 and m = 100. (Show your work.)
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Step 1
In other words, we want to find an integer $x$ such that $53x \equiv 1 \pmod{100}$. Step 2: We can rewrite the congruence as $53x - 100y = 1$ for some integer $y$. This is a linear Diophantine equation. Step 3: Apply the Extended Euclidean Algorithm to find the Show more…
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