Groups
Category
Level
A linear Diophantine equation ax + by = c has integer solutions if and only if gcd(a, b) divides c.
A modular inverse of a modulo m is a number a_inv such that a × a_inv ≡ 1 (mod m).
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).