Why it matters

Extended Euclidean enables modular arithmetic. Understanding shapes crypto + CRT.

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The architecture

Track (u, v) coefficients through Euclidean recursion.

Return (gcd, u, v).

Extended Euclidean structureEuclidean recursionwith (u, v) trackingBack-substitutecoefficientsReturn gcd + u + vBezout identityModular inverse: a^-1 mod m = u when gcd(a, m) = 1
Extended Euclidean.
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How it works end to end

Recursion or iteration.

Modular inverse: gcd = 1, then u is inverse.

CRT construction uses.