Groups
Category
Level
Lucas' Theorem lets you compute C(n, k) modulo a prime p by working digit-by-digit in base p.
Eulerโs Theorem says that if a and n are coprime, then a raised to the power ฯ(n) is congruent to 1 modulo n.
The Chinese Remainder Theorem (CRT) reconstructs an integer from its remainders modulo pairwise coprime moduli and guarantees a unique answer modulo the product.
The Extended Euclidean Algorithm finds integers x and y such that ax + by = gcd(a, b) while also computing gcd(a, b).