Subject: Mathematics
Book: Maths Mastery
A modular inverse of a number a (mod m) is x such that ax ≡ 1 (mod m). It exists only if gcd(a,m)=1. The Extended Euclidean Algorithm finds x for which ax + my=1, implying ax≡1 (mod m). For instance, to find the inverse of 3 modulo 7, we solve 3x + 7y=1, yielding x=5 because 3×5=15≡1 (mod 7). Modular inverses power encryption algorithms (RSA), solve congruences, and handle advanced computations in computer science. Mastery ensures you can manipulate modular arithmetic quickly for a wide range of cryptographic and number-theoretic tasks.
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