Modular inverse
Find a⁻¹ mod m — the number x where ax ≡ 1 (mod m). Essential for RSA and modular arithmetic.
a =mod
What is a modular inverse?
a⁻¹ mod m is the number x where ax ≡ 1 (mod m). It exists only when GCD(a, m) = 1 (a and m are coprime).
3⁻¹ mod 7: 3×5 = 15 ≡ 1 (mod 7) → 3⁻¹ ≡ 5 (mod 7).
Finding it
Use the extended Euclidean algorithm to find x in ax + my = 1, then x mod m is the inverse.
Applications
RSA encryption, solving linear congruences, Chinese Remainder Theorem.
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