Groups
Category
Level
Lucas' Theorem lets you compute C(n, k) modulo a prime p by working digit-by-digit in base p.
A linear Diophantine equation ax + by = c has integer solutions if and only if gcd(a, b) divides c.
The discrete logarithm problem asks for x such that g^x ≡ h (mod p) in a multiplicative group modulo a prime p.
The Chinese Remainder Theorem (CRT) reconstructs an integer from its remainders modulo pairwise coprime moduli and guarantees a unique answer modulo the product.